tsr 

LABORATORY 

OF  PHY 

S,  ;   .  C  ( ) I 


RARY  OF 


u  a 


GIFT   OF 


UNIVERSITY  FARM 


NEW 

LABORATORY  MANUAL 
OF  PHYSICS 


BY 


S.   E.   COLEMAN,  S.B.,  A.M. 

HEAD   OF  THE    SCIENCE   DEPARTMENT,    AND   TEACHER   OF 
PHYSICS   IN   THE  OAKLAND    HIGH    SCHOOL 


NEW  YORK  . : .  CINCINNATI . : .  CHICAGO 

AMERICAN    BOOK    COMPANY 
UNIVERSITY  OF  CALIFORNIA 

LIBRARY 

BRANCH  OF  THE 
COLLEGE  OF  AGRICULTURE 


COPYRIGHT,  1908,  BY 
S.    E.   COLEMAN. 

ENTERED  AT  STATIONERS'  HALL,  LONDON,, 


COLEMAN'S  NEW  LAB.  MAN. 
w.  P.    7 


PREFACE 

THAT  laboratory  work  is  an  important  part  of  a  course  in 
elementary  physics  is  no  longer  open  to  question.  The  opinion 
is  also  practically  unanimous  that  the  laboratory  work  should 
constitute  an  organic  and  integral  part  of  the  course,  pursued 
concurrently  with  the  instruction  of  the  class  room  throughout 
the  subject.  Beyond  this  point,  however,  there  is  still  a  con- 
siderable diversity  of  opinion  and  practice  within  the  limits  of 
good  teaching.  While  the  author  believes  that  this  Manual 
will  be  found  adapted  to  any  approved  plan  of  work,  it  will  not 
be  out  of  place  to  present  the  point  of  view  from  which  the  book 
was  written. 

Its  scope  is  that  of  a  laboratory  guide  for  the  pupil.  It  en- 
croaches as  little  as  possible  on  the  province  of  the  text-book, 
and  does  not  include  class-room  experiments  to  be  performed 
by  the  teacher.  Many  such  experiments  must  be  presented 
in  any  well-conducted  course  in  physics  ;  but  it  is  unnecessary  to 
place  the  directions  for  them  in  the  hands  of  the  pupils. 

Every  experiment  in  the  course  is  a  physical  experiment. 
With  a  superabundance  of  excellent  material  within  the  scope 
of  elementary  physics,  there  would  seem  to  be  no  valid  reason . 
for  spending  the  first  days  in  the  laboratory  on  manipulation 
and  measurement  with  vernier  and  micrometer  calipers,  the 
diagonal  scale,  the  spherometer,  etc.,  as  is  sometimes  done,  with 
no  physics  in  sight. 

The  course  aims  to  present  a  maximum  of  physics  with  a 
minimum  of  manipulation.  So  far  as  the  teaching  of  elementary 
science  is  concerned,  skill  in  manipulation  must  be  regarded 
as  a  means  to  an  end,  not  as  an  end  in  itself.  The  more  simply 

3 

/?3ft 


4  PREFACE 

and  directly  a  physical  problem  is  presented  to  the  pupil  the 
better,  that  his  thought  and  attention  may  not  be  diverted  from 
the  real  point  at  issue.  This  principle  is  especially  applicable 
in  the  early  part  of  the  laboratory  course,  where  it  is  most 
frequently  and  most  seriously  violated  by  the  use  of  micrometric 
instruments,  the  Jolly  balance,  etc.,  in  the  work  on  density  and 
specific  gravity,  eyen  before  the  pupil  has  had  practice  in  the 
simpler  methods  of  measuring  and  weighing.  It  would  seem 
as  if  the  express  purpose  of  such  work  were  at  the  outset  to 
throw  as  many  obstacles  in  the  way  of  progress  in  physics  as 
the  ingenuity  of  teachers  and  instrument  makers  could  devise. 

To  be  entitled  to  a  place,  a  laboratory  experiment  must  serve 
a  definite  purpose  in  the  general  plan  of  the  course ;  it  must 
contribute  something  of  value  in  the  unfolding  of  that  plan. 
Perhaps  the  most  striking  illustration  of  what  should  not  be 
done  in  this  respect  is  afforded  by  the  familiar  quantitative 
experiments  on  the  breaking  strength  of  wires  and  on  elasticity 
of  stretching,  bending,  and  twisting.  These  experiments  lead 
absolutely  to  nothing  in  most  high-school  courses.  The  laws 
with  which  they  deal  are,  for  the  most  part,  not  considered  in 
elementary  text-books.  A  simple  qualitative  treatment  in  the 
class  room  or  the  laboratory  would  serve  as  an  ample  experi- 
mental basis  for  all  the  applications  that  are  or  need  be  con- 
sidered in  a  general  high-school  course. 

The  qualitative  experimental  study  of  phenomena  rightly  de- 
mands a  large  place  in  an  elementary  physics  course.  Economy 
of  time  and  equipment,  convenience,  and  the  advantage  of  the 
superior  skill  of  the  teacher,  are  considerations  in  favor  of  pre- 
senting much  of  this  material  in  the  form  of  class-room  experi- 
ments ;  but  in  a  great  many  instances  the  laboratory  experiment, 
affording,  as  it  does,  immediate  sense  perception  of  the  phe- 
nomena in  their  simplest  aspects  and  at  close  range,  is  .greatly 
superior  to  any  experiment  viewed  at  a  distance ;  and  a  labora- 
tory course  which  fails  to  take  this  into  account  is  necessarily 
one-sided  and  incomplete.  No  apology  is  therefore  necessary 


PREFACE  5 

for  the  large  number  of  qualitative  experiments  in  this  Manual. 
They  are  entitled  to  consideration.  To  lessen  the  burden  of 
the  laboratory  record,  which  rests  rather  heavily  on  teacher  and 
pupil  alike,  it  is  suggested  that  many  of  the  qualitative  experi- 
ments may  be  made  nearly,  if  not  quite,  as  valuable  a  part  of 
the  laboratory  course  without  requiring  a  written  record  of  them. 
In  such  cases  the  discussion  of  the  observed  phenomena  in  the 
recitation  will  suffice. 

Physics  should  be  so  taught  that  the  pupil  will  be  led  to  a 
correct  view  of  the  significance  of  his  laboratory  work  in  its 
relation  to  the  subject  as  a  science.  He  should  understand 
that  the  validity  of  scientific  generalizations,  particularly  those 
of  a  quantitative  character,  does  not  depend  upon  the  neces- 
sarily inaccurate  and  incomplete  data  gathered  from  the  experi- 
ments of  the  class  room  and  the  laboratory.  These  experiments 
should  be  regarded  as  a  limited  inquiry  into  the  facts  at  first 
hand,  not  as  sources  of  adequate  data  for  generalizations  by  the 
pupil,  nor  as  "verifications"  of  the  laws  and  principles  stated  in 
the  text.  The  pupil's  experiment  is  not  a  proof  of  the  law,  but  an 
aid  to  the  right  understanding  of  it.  For  example,  under  Boyle's 
law  the  pupil  performs  an  experiment  with  one  gas  only  (air), 
at  one  temperature  only,  and  with  only  a  moderate  range  of 
pressure.  With  the  apparatus  ordinarily  provided,  the  work 
is  well  done  if  it  is  not  in  error  by  more  than  two  per  cent.  It 
would  be  no  less  than  a  complete  perversion  of  the  distinctive 
aims  and  purposes  of  scientific  instruction  to  lead  the  pupil 
to  regard  such  an  experiment  as  a  verification  or  proof  of  Boyle's 
law ;  namely,  that  the  inverse  proportionality  of  volume  and 
pressure  is  true  (accurately  true)  for  all  gases  at  any  temperature 
and  under  all  ranges  of  pressure.  It  is  hardly  necessary  to  say 
that  Boyle's  law  is  not  verified  until  the  experiment  is  repeated 
at  many  different  temperatures  with  every  gas,  and  performed 
with  an  accuracy  equal  to  that  of  the  ablest  experimenters.  It 
would  then  be  found  (as  the  texts  state)  that  the  usual  state- 
ment of  the  law  is  not  exact,  and  that  it  wholly  fails  for  any  gas 


6  PREFACE 

when  near  a  temperature  and  pressure  at  which  it  liquefies. 
Since  the  pupil  does  not  undertake  such  an  investigation,  he 
neither  proves  nor  disproves  the  law.  What  he  really  does 
is  to  perform  an  experiment  which,  within  a  fair  degree  of 
accuracy,  illustrates  or  exemplifies  the  law ;  and  he  does  this 
in  order  that  he  may  the  better  understand  it,  not  because  the 
law  is  in  need  of  "  verification."  . 

It  is  of 'course  true  that  the  laboratory  work  affords  a  suffi- 
cient basis  for  important  inferences  and  conclusions ;  but  these 
are  necessarily  simple,  and  generally  narrow  and  partial.  They 
must  be  limited  to  what  follows  legitimately  from  the  experi- 
mental data.  To  encourage  the  pupil  to  draw  hasty  and  unwar- 
ranted conclusions  from  insufficient  data  is  a  vicious  practice. 

This  point  of  view  concerning  the  function  of  experimental 
work  in  elementary  physics  is  maintained  throughout  the  Manual, 
particularly  in  the  statement  of  the  purpose  of  each  experiment 
and  in  the  questions  asked  in  the  discussions.  Consistently 
with  the  view  that  the  laboratory  course  is  not  a  sufficient  basis 
from  which  to  evolve  physics  as  a  science,  it  is  assumed  in  the 
discussion  of  experimental  results  that  the  pupil  has  at  least 
carefully  read  his  text-book  on  the  subject  of  the  experiment, 
and  is  therefore  in  a  position  not  only  to  state  the  conclusions 
which  are  supported  by  his  work,  but  also  to  pass  judgment  on 
the  quality  of  it  by  comparing  his  results  with  those  known  to 
be  correct. 

To  provide  opportunity  for  choice  and  to  increase  the  adapt- 
ability of  the  Manual  to  the  varying  equipment  of  different 
laboratories,  the  number  of  exercises  has  been  made  considerably 
greater  than  most  teachers  will  require  in  a  one-year  course. 
A  course  of  sixty  exercises,  properly  distributed  over  the  differ- 
ent parts  of  the  subject,  would  constitute  a  liberal  provision  of 
laboratory  work,  and  fifty  exercises  a  reasonable  minimum. 
The  following  exercises  are  suggested  as,  on  the  whole,  the  best 
adapted  to  such  a  minimum  course,  having  regard  to  the  cost 
of  equipment  and  also  to  the  fact  that  many  of  the  experiments, 


PREFACE  7 

or  others  serving  the  same  purpose,  can  be  performed  by  the 
teacher  before  the  class,  with  satisfactory  results :  Exercises  1-5, 
6  (any  two  of  the  four  experiments),  7,  9,  10,  n  or  12,  13,  14, 
16  or  17,  19  or  21,  20,  23-25,  26  (Exp.  50),  29-34,  36,  any  two 
of  37  to  41,  42,  43>  45>  47~52>  54  or  55,  56,  57-63,  64  (either 
experiment),  66  (any  one  of  the  experiments),  70,  73. 

The  experiments  have  been  chosen  and  planned  with  due 
regard  to  a  reasonable  economy  in  the  equipment  of  the  labora- 
tory and  a  moderate  degree  of  accuracy  in  quantitative  results. 
It  is  far  better  to  have  from  two  to  six  sets  of  apparatus  of 
medium  cost  for  each  experiment,  so  that  the  entire  class  can 
be  accommodated  without  running  more  than  from  two  to  four 
exercises  simultaneously,  than  to  provide  only  one  set  of  expen- 
sive apparatus  for  each  experiment.  On  the  other  hand,  it  is 
not  a  wise  economy  to  spend  money  on  cheap  apparatus,  lacking 
in  durability  and  efficiency.  The  instruments  shown  in  the  cuts 
throughout  the  book  are  recommended  as  of  satisfactory  grade. 

The  grouping  of  related  experiments  into  exercises  will  com- 
mend itself  as  a  convenience  both  to  teacher  and  pupil.  It  is 
intended  that,  in  the  regular  progress  of  the  work,  one  laboratory 
period  (either  single  or  double)  will  be  devoted  to  each  exercise. 
The  whole  of  a  single  laboratory  period  will  ordinarily  be  re- 
quired for  the  experimental  work  of  the  exercise,  with  only  a 
preliminary  record  of  it  in  the  form  of  rough  notes ;  and  time 
outside  the  laboratory  must  be  taken  for  writing  the  permanent 
record.  A  double  laboratory  period  (an  hour  and  a  half)  should 
be  sufficient  for  both  the  experimental  work  and  the  final  record. 

While  the  present  work  is  in  greater  part  a  revision  of  the " 
author's  "  Physical  Laboratory  Manual,"  it   is    newly   written 
throughout ;   and  full  advantage  has  been  taken  of  the  oppor- 
tunity to    make    the    many  improvements    in    subject-matter, 
arrangement,  and  presentation  which  have  been  made  possible 

by  later  years  of  experience. 

S.    E.   COLEMAN. 

OAKLAND,  CALIFORNIA. 


CONTENTS 


I.    GENERAL  DIRECTIONS 


The  Laboratory  Work     . 
The  Laboratory  Record  . 


PAGE 
II 

13 


Computations 14 

Measurements    ......       19 


II.     DENSITY 


EXERCISE 


I.  Density  of  Solids  .     ...       24         2.   Density  of  Liquids    ...      26 
III.     MECHANICS   OF  FLUIDS 


3.  Gravity  Pressure  in  Liquids  29 

4.  Buoyancy  of  Liquids      .     .  31 

5.  Specific  Gravity  of  Solids  .  34 

6.  Specific  Gravity  of  Liquids  36 


7.  Pressure  of  Gases      ...  40 

8.  Boyle's  Law 43 

9.  The  Suction  Pump  and  the 

Siphon 46 


IV.     STATICS  OF   SOLIDS 


10.  Equilibrium  of  Concurrent 

Forces 49 

11.  Equilibrium     of     Parallel 

Forces 52 

12.  Moments  of  Force    ...       56 


59 


13.  Center  of  Gravity  and  Mo- 

ment of  Weight     .     .     . 

14.  Center  of  Gravity  and  the 

States  of  Equilibrium      .       62 

15.  Stiffness   of  Beams.      The 

Truss 64 


V.     DYNAMICS  AND   MACHINES 


1 6.  Falling  Bodies :    Whiting's 

Method 67 

17.  Falling  Bodies:    Packard's 

Method 69 

1 8.  The  Simple  Pendulum  .     .       73 


19.  The  Wheel  and  Axle 

20.  Pulleys 

21.  The  Inclined  Plane  . 

22.  Geared  Wheels     .     . 


76 
so 
83 
85 


VI.     MOLECULAR   PHENOMENA 


23.   Cohesion  and  Adhesion 


86 


24.    Surface  Tension  and  Capil- 
larity   88 


CONTENTS 


VII.     HEAT 


EXERCISE  PAGE 

25.  Conduction  and  Convection  91 

26.  Radiant  Energy    ....  93 

27.  Coefficient   of  Linear    Ex- 

pansion      96 

28.  Coefficient  of  Expansion  of 

Air 99 

29.  Specific  Heat 101 

30.  Melting  and  Freezing    .     .  104 


EXERCISE  PAGE 

31.  Heat  of  Fusion  and  Solu- 

tion       106 

32.  Cooling    by    Evaporation ; 

Dew-point 109 

33.  Phenomena  of  Boiling  .     .  m 

34.  Heat    of    Vaporization    of 

Water 114 

35.  The  Steam  Engine    .     .     .  116 


VIII.     SOUND 


36.  The  Transmission  of  Sound  1 18 

37.  Ripples.        Reflection     of 

Sound 121 

38.  Vibration  Number  of  a  Fork  124 

39.  Interference  and  Beats  .     .  126 


129 


40.  The  Law  of  Lengths 

41.  Sympathetic    and    Forced 

Vibrations 130 

42.  Wave  Length  by  Resonance     133 


IX.     LIGHT 


Shadows;  Pin-hole  Images; 
Law  of  Intensity  .  .  .  136 

Photometry 139 

Plane  Mirrors 143 

46.  Multiple  Images   ....     148 

47.  The  Concave  Mirror      .     .     149 
Phenomena  due  to  Refrac- 
tion      153 

Snell's  Law  of  Refraction  ; 
Index  of  Refraction  of 
Glass 157 


43 

44, 
45- 


48. 


49, 


50.  Refraction  through  a  Plate 

and    through   a    Prism ; 
Total  Reflection    .     .     .     161 

51.  The  Convex  Lens      .     .     .     165 

52.  Convex  and  Concave  Lenses     168 

53.  The  Eye 171 

54.  The  Simple  and  the  Com- 

pound Microscope      .     .     1 72 

55.  The  Astronomical  and  the 

Galilean  Telescope     .     .     176 

56.  The  Spectrum;   Color  .     .     179 


57.    Magnets     and      Magnetic 

Action  i 


X.     MAGNETISM 

58.    Magnetic  Fields  . 


188 


XI.     ELECTRICITY 


59.  The  Simple  Voltaic  Cell     .     191 

60.  The   Magnetic   Field   of  a 

Current 194 


61.  The  Helix,  the  Electro- 
magnet, and  the  Electric 
Bell 


I97 


10 


CONTENTS 


EXERCISE  PAGE 

62.  The  Electric  Telegraph      .     200 

63.  The        Tangent        Galva- 

nometer; Polarizing,  and 
Nonpolarizing  or  Con- 
stant Cells 202 

64.  Measurement  of  Resistance 

by  Substitution ;  The 
Laws  of  Resistance  .  .  209 

65.  The  Resistance  of  a  Cell    .     213 

66.  The  Electro-motive   Force 

of  Cells 216 

67.  The   Electro-motive   Force 

and  Resistance  of  a  Cell      221 

68.  The  Fall  of  Potential  along 

a  Conductor      ....     222 


EXERCISE  PAGE 

69.    Measurement  of  Resistance 
with      the      Wheatstone 
Bridge      ......     226 

Arrangement  of  Cells     .     .     232 
Measurement  of  Electrical 

Power 235 

Induced  Currents  ....     238 
The    Electric     Motor    and 

Dynamo 241 

The  Gilley   Gramme   Ring 

Dynamo  and  Motor   .     .     246 

75.  The  Telephone     .     .     .     ,     251 

76.  Electrolysis  and  the  Storage 

Cell 254 


70. 
71- 

72. 
73- 

74- 


APPENDIX  . 


259 


Special  catalogues  of  the  apparatus  for  this  manual  are  issued  by  the 
University  Apparatus  Co.,  2229  McGee  Ave.,  Berkeley,  California  ;  and  by  the 
Chicago  Apparatus  Co.,  557-559  W.  Quincy  St.,  Chicago,  Illinois. 


NEW   LABORATORY    MANUAL 
OF    PHYSICS 

I.     GENERAL    DIRECTIONS 

1.  The  following  general  directions  should  be  carefully  studied 
before  the  laboratory  work  is  begun.    It  is  not  to  be  expected  that 
they  will  all  be  fully  understood  until,  by  actual  experience  in  the 
laboratory,  the  pupil  has  become  somewhat  acquainted  with  the 
various  matters  with  which  they  deal.     It  will  therefore  be  neces- 
sary to  refer  to  them  frequently  during  the  first  few  weeks,  until 
they  become  thoroughly  familiar. 

THE  LABORATORY  WORK 

2.  Preparation.  —  Finish  the  record  of  each  laboratory. exercise 
before  beginning  the  next.     It  is  generally  impossible  to  perform 
an  experiment  intelligently  unless  the  lessons  to  be  drawn  from  the 
experiments  immediately  preceding  have  been  definitely  learned. 

If  the  subject  with  which  the  exercise  deals  is  not  already 
familiar  from  previous  class-room  work,  read  the  text-book  on  the 
subject  before  the  laboratory  period.  Read  also  the  laboratory 
directions  for  the  exercise.  The  preliminary  information  thus 
gained  lessens  the  danger  of  misdirected  effort  in  the  laboratory 
and  makes  the  work  much  easier  to  understand. 

The  references  indicated  at  the  beginning  of  each  exercise  may 
be  consulted  during  the  laboratory  period,  as  opportunity  offers, 
or  at  such  other  times  as  the  instructor  may  direct. 

To  save  time  in  the  laboratory,  tabular  forms  for  the  record  of 
measurements  should  be  prepared  in  advance. 

3.  Apparatus.  —  Before    beginning   an    exercise   note  whether 
you  have  everything  called  for  in  the  list  of  apparatus.     If  any- 


12  GENERAL   DIRECTIONS 

thing  is  missing  or  unsatisfactory,  report  the  fact  to  the  instructor 
at  once.  Never  take  apparatus  from  other  places  than  your 
own. 

4.  Neatness  and  Order.  —  A  very  important  incidental  benefit 
of  a  properly  conducted  laboratory  course  is  the  training  it  affords 
in  neatness  and  order.     Pupils  should  feel  a  personal  responsibil- 
ity for  the  condition  of  the  apparatus  and  table  where  they  are  at 
work,  and  especially  for  the  condition  in  which  these  are  left  at 
the  end  of  the  hour.     A  proper  regard  for  the  comfort  and  con- 
venience of  others  demands  that  you  leave  the  place  you  have 
occupied  at  least  as  clean  and  orderly  as  you  found  it. 

5.  Damage  to  Apparatus.  —  Pupils  are  responsible  for  all  dam- 
age  to   apparatus    in  their  possession,  and   should  report  such 
damage  to  the  instructor  immediately. 

6.  Economy  of  Time  in  the  Laboratory.  —  It  is  expected  that 
each  exercise  will  be  completed  in  one  laboratory  period.     To 
make  sure  of  accomplishing  this,  no  time  should  be  taken  in  the 
laboratory  for   writing   discussions  or  for  making   computations 
(unless  the  results  of  these  computations  are  needed  at  the  time), 
until  the  exercise  for  the  day  is  completed.     The  remainder  of 
the  period  may  be  spent  either  in  reading  the  references  or  in 
writing  up  the  exercise.     No  time  should  be  wasted. 

7.  Questions. —  Numerous  questions  are  interspersed  with  the 
directions  for  the  experimental  work.     Do  not  pass  over  these 
questions,  leaving  them  for  later  consideration.     They  direct  the 
attention  to  matters  that  should  be  understood  at  the  time  —  with 
the  assistance  of  the  teacher,  if  necessary.     The  answers  to  ques- 
tions in  parentheses  may  be  omitted  from  the  record. 

8.  Repetition   of  Work.  —  An  experiment  is  to  be   repeated 
when  the  results  are  unsatisfactory.     Present  doubtful  results  to 
the  teacher  for  his  decision  as  soon  as  possible,  so  that  the  experi- 
ment may  be  repeated,  if  necessary,  without  delay. 


THE  LABORATORY  RECORD  13 

THE  LABORATORY  RECORD 

9.  Specific  Directions  concerning  the  manner  of  taking  notes 
during  the  progress  of  experimental  work  and  the  form  and  scope 
of  the  final  record  will  be  given  by  the  teacher.     In  addition  to 
these,  the  following  general  directions  should  be  carefully  observed. 

10.  General  Form.  —  Copy  the  number  and  title  of  each  exer- 
cise and  the  purpose  of  each  experiment  (printed  in  italics)  from 
the  manual ;  and  arrange  the  notes  on  each  experiment  under  the 
various  heads  there  indicated.     Give  proper  attention  to  regular- 
ity of  margins,  paragraphing,  spacing,  numbering,  lettering,  etc. 
Do  not  crowd  the  notes.    Leave  a  vacant  line  between  the  experi- 
ments of  an  exercise,  and  several  vacant  lines  between  exercises. 
Make  headings  prominent.     In  all  these  matters  of  general  form 
the  record  should  correspond  with  the  manual. 

Measurements,  computations,  and  numerical  results  should 
always  be  set  apart  by  themselves,  so  as  to  be  easily  seen  and  com- 
pared. Sets  of  numbers  are  best  entered  in  columns,  as  in  Exer- 
cises i,  8,  n,  12,  etc.  Single  items  should  be  given  one  or  more 
whole  lines  each,  with  the  numbers  at  the  right-hand  side  of  the 
page,  as  in  Exercises  i,  2,  4,  5,  etc.  When  no  form  of  record  is 
given  for  an  experiment,  devise  a  satisfactory  one  for  yourself. 

N)ll.  Clearness  and  Brevity.  —  The  record  should  be  complete 
in  itself,  i.e.  should  not  require  a  knowledge  of  the  directions  or 
the  questions  asked  in  the  manual  to  make  it  fully  intelligible. 
It  should  be  as  brief  as  possible  without  sacrificing  clearness  or 
omitting  essentials.  The  answers  to  questions  inclosed  in  paren- 
theses may  be  omitted  from  the  record ;  but  these  questions 
should  receive  no  less  careful  attention  on  that  account.  Be  pre- 
pared to  answer  them  orally  at  any  time. 

12.    Decimals.  —  Express   all   fractional    quantities    decimally. 
-The  relative  values  of  fractions  expressed  decimally  can  be  de- 
termined at  a  glance,  but  in  the  form  of  common  fractions  this  is 
generally  impossible.     In  the  actual  work  of  measuring  and  com- 


14  GENERAL   DIRECTIONS 

puting,  the  decimal  fraction  is  almost  without  exception  more  con- 
venient than  the  common  fraction.  This  is  especially  true  in 
using  the  metric  system. 

Express  a  quantity  in  terms  of  one  unit  only  ;  e.g.  write  15.25  g. 
instead  of  15  g.  2  dg.  5  eg.  Express  all  lengths  in  centimeters. 

13.  What    constitutes   an   Honest   Record.  —  Your   laboratory 
notes  are  accepted  upon   the  supposition   that  they  are   a  true 
record  of  the  work  done  by  you  in  the  laboratory.     If  the  results 
are  not  satisfactory,  the  only  remedy  is  to  repeat  the  experiment. 
Neither  borrowing  nor  lending  of  note  books  can  be  permitted. 
Where  pupils  work  in  pairs  each  should  always  take  a  complete 
record  of  all  measurements  and  other  necessary  data,  so  as  to  be 
wholly  independent  of  his  laboratory  mate  in  writing  up  the  ex- 
ercise, and   each  should  perform  all  computations    for   himself. 
Pupils  may,  of  course,  give  one  another  the  kind  of  help  that  they 
might  expect  from  the  teacher. 

COMPUTATIONS 

14.  The  Record   of   Computations.  —  The   mathematical   pro- 
cesses by  which  computed  results  are  obtained  must  either  be 
fully  recorded  or  indicated  by  means  of  the  signs  of  addition,  sub- 
traction,  etc.     In  the  first  two  exercises  the  computations  are 
indicated  in  the  model  form  of  record,  parentheses  being  used 
to  represent  the  numbers.     You  are  expected  to  remember  this 
direction  and  to  observe  it  in  all  subsequent  work  without  such  a 
reminder. 

Where  results  are  entered  in  tabular  form,  and  the  computations 
indicated  at  the  tops  of  the  columns,  only  the  results  are  to  be 
entered  in  the  columns. 

15.  Concrete  Numbers.  —  The  name  of  the  unit  should  always 
be  written  after  the  numerical  value  of  a  measured  or  computed 
quantity.     This  applies  to  each  quantity  recorded  in  a  series  of 
computations  as  well  as  to  the  final  result.     Failure  to  keep  track 
of  the  physical  units  involved  in  computations  is  a  fruitful  source 


COMPUTATIONS  1 5 

of  errors  in  the  solution  of  problems  as  well  as  in  the  laboratory 
work. 

16.  Testing  Numerical  Results.  —  When  an  experiment  leads 
to  a  numerical  result  the  true  value  of  which  is  known,  —  as  the 
weight  of  a  cubic  centimeter  of  pure  cold  water  (Experiment  3),  — 
a  comparison  of  the  experimental  value  with  the  true  value  of  the 
quantity  serves  as  a  check  on  the  work,  to  determine  whether  it 
has  been  done  with  reasonable  care  and  accuracy.     The  method 
of  making   such   a   comparison   is   illustrated   by   the   following 
example. 

If  a  length  of  10.05  cm.  is  measured  and  recorded  as  10  cm., 
the  error  is  .05.  This  is  .05-^-10.05,  or  .005,  of  the  quantity 
measured,  or  .5%  of  it.  An  equal  error  (.05  cm.)  in  measuring  a 
length  of  2.5  cm.  is  2  %  of  the  quantity  measured.  In  the  second 
case  the  error  is  of  more  consequence  because  it  is  a  larger 
fraction  of  the  quantity  measured.  To  illustrate  further,  if  an 
error  of  only  an  inch  were  made  in  measuring  off  a  mile,  the  work 
would  be  considered  very  accurate ;  but  the  measured  height 
of  a  table  would  be  very  inaccurate  if  it  were  in  error  by  as  much 
as  an  inch.  It  will  be  seen  that  the  degree  of  accuracy  of  a  meas- 
urement is  not  expressed  by  the  error,  but  by  the  percentage  of^ 
error. 

If  the  percentage  of  error  of  any  result  is  unreasonably  large, 
the  experiment  should  be  repeated  as  soon  as  possible.  Only 
reasonably  accurate  results  should  be  handed  in  for  inspection. 

17.  How  the  Accuracy  of  Measurements  enters  into  Computa- 
tions. —  To  retain  either  more  or  fewer  decimal  places  in  a  com- 
puted result  than  the  accuracy  of  the  measurements  justifies  is  an 
error  to  be  carefully  avoided.     The  principles  and  rules  governing 
correct  practice  in  this  matter  are  illustrated  in   the   following 
examples. 

In  the  first  laboratory  exercise  it  is  required  to  determine  the 
volume  of  a  rectangular  solid.  The  length  is  measured  near  each 
of  the  four  edges  extending  in  that  direction,  and  the  values 


l6  GENERAL   DIRECTIOiNS 

found  are,  let  us  say,  7.25  cm.,  7.23  cm.,  7.24  cm.,  and  7.23  cm. 
The  average  of  these  numbers  is  7.2375  cm.  Now  the  last  figure 
in  each  of  the  four  measurements  is  doubtful,  the  estimate  of 
hundredths  of  a  centimeter  (or  tenths  of  a  millimeter)  being  un- 
certain by  at  least  one  or  two  hundredths ;  hence  the  3  in  the 
second  decimal  place  of  the  average  is  doubtful,  and  the  last  two 
figures  should  be  dropped.  But  since  the  first  figure  discarded  is 
greater  than  5,  the  last  figure  retained  is  increased  by  one ;  i.e.  the 
average  is  written  7.24  cm.  To  retain  the  four  decimal  places 
would  be  wrong,  since  this  would  imply  a  greater  accuracy  than 
was  actually  attained  in  the  measurements.  It  would  also  be 
wrong  to  drop  all  but  the  first  decimal  figure,  since  we  have  good 
reason  for  thinking  that  7.24  cm.  is  more  nearly  right  than  7.2  cm. 

Let  us  suppose  further  that  the  average  width  of  the  solid  is 
found  to  be  5.78  cm.,  and  the  average  thickness  3.18  cm. 

The  volume  of  the  body  =  7.24  X  5.78  X  3.18  c.c. 

7.24  41.8 

5.78  3-18 

5792  3  344 

5  068  4  18 

36  20  125  4 

41.8472  132-924 

In  the  above  work  the  doubtful  figures  are  printed  in  heavy- 
faced  type.  Thus,  in  the  first  multiplication,  since  the  last  figure, 
8,  of  the  multiplier  is  in  doubt,  all  that  depends  upon  it  is  in  doubt, 
t.e.  the  entire  product,  .5792.  The  volume  of  the  body  should  be 
written  133  c.c. 

It  is  easy  to  see  from  this  example  why  unreliable  figures  accu- 
mulate in  multiplication  ;  but  in  seeking  a  practical  rule  by  which 
to  determine  what  figures  should  be  retained,  we  must  study  the 
question  from  a  different  point  of  view.  Suppose  in  the  above  ex- 
ample that  each  dimension  of  the  block  is  in  doubt  by  .02  cm.  This 
uncertainty,  or  possible  error,  is  about  y^  of  the  length,  -g-^-g-  of  the 
width,  and  -%%-$  of  the  thickness.  The  possible  error  of  the  product 


COMPUTATIONS 


is  the  sum  of  the  possible  errors  of  all  the  factors,  i.e.  j^  -f-  ¥^  -f- 
3T o">  or  TTTO  >  or  (roughly)  a  li^6  more  than  i  %  •  This  clearly 
renders  the  units'  figure  of  the  computed  volume  doubtful.  If  we 
suppose  each  dimension  of  the  block  to  be  in  doubt  by  only  .01  cm., 
the  product  will  be  in  doubt  by  about  -|  %  ;  and,  as  this  also 
makes  the  units'  figure  of  the  product  doubtful,  the  result  should 
still  be  written  133  c.c.  We  should,  however,  be  justified  in  re- 
taining the  first  decimal  place  in  the  computed  volume  if  we  had 
reason  to  believe  that  the  probable  error  of  each  factor  was  less 
than  .01  cm. 

The  following  table  shows  how  the  computed  values  given  in  the 
first  column  should  be  written  when  the  probable  error  is  less  than 
i  %,  when  it  is  between  i  %  and  2  %,  and  when  it  is  over  2  %. 


COMPUTED  VALUE 

ERROR  UNDER  i% 

ERROR  OF  i%  TO  2% 

ERROR  OVER  2% 

214.27 

214.3 

2I4. 

214 

93.628 

93-6 

93-6 

94 

10-354 

10-35 

10-35 

10.4 

.09567 

.0957 

.096 

.096 

As  a  general  rule,  computations  should  be  carried  to  the  first 
doubtful  figure,  and  all  decimal  places  beyond  this  should  be  dis- 
carded ;  but  in  some  cases  the  first  two  doubtful  figures  should  be 
retained.  For  example,  if  the  true  value  of  a  quantity  is  1.19  and 
the  pupil's  value  is  1.2263,  his  answer  should  be  written  1.23,  not 
1.2  ;  for  although  the  first  decimal  figure  is  in  error,  the  omission 
of  the  next  figure  would  change  the  value  of  the  result  by  2.5  %,, 
which  is  nearly  as  great  as  the  experimental  error.  The  omission 
of  the  .03  would  therefore  mask  the  true  quality  of  the  experimen- 
tal work. 

-  In  division  the  possible  percentage  of  error  of  the  quotient  is  the 
sum  of  the  possible  percentage  of  error  of  the  divisor  and  dividend, 
and  the  same  rule  holds  for  retaining  decimal  places  as  in  multi- 
plication. The  division  should  always  be  carried  far  enough  to 
determine  whether  the  first  discarded  decimal  figure  is  greater  or 
COLEMAN'S  NEW  MANUAL  —  2 


1 8  GENERAL   DIRECTIONS 

less  than  5.  If  it  is  5  or  greater,  the  last  figure  retained  is  increased 
by  one,  as  in  the  above  examples. 

When  a  result  depends  upon  a  series  of  computations,  each 
computation  must  be  carried  far  enough  to  avoid  introducing  any 
appreciable  error  into  the  work.  The  safest  plan  for  the  beginner 
is  to  carry  decimal  places  in  excess  throughout  the  computations, 
and  to  discard  them  only  in  the  final  result. 

18.  Detecting  Errors  of  Computation.  —  Decimal  points  are  fre- 
quently misplaced.     A  mere  glance  at  the  numbers  is  generally 
sufficient  to  detect  such  an  error.     Thus,  if  38.2  be  divided  by 
.094,  it  will  be  evident  at  once  that  the  quotient  is  slightly  greater 
than  ten  times  the  dividend  (since  the  divisor  is  slightly  less  than 
.1),  and  that,  if  the  quotient  is  written  40.64  or  4064.,  the  decimal 
point  is  misplaced. 

Misplaced  decimal  points  and  other  gross  errors  of  computation 
can  often  be  detected  by  the  absurdity  of  the  results.  Thus  if  one 
should  get  .412  g.  as  the  weight  of  i  c.c.  of  a  stone  in  Experiment 
2,  he  should  know  at  once  that  a  serious  blunder  had  been  made 
either  in  the  experimental  work  or  in  the  computation ;  for  this  is 
less  than  half  the  weight  of  i  c.c.  of  water  (i  g.),  and  the  pupil 
knows  that,  for  equal  bulk,  stone  is  much  heavier  than  water. 

The  capable  student  will  soon  realize  that,  in  such  matters  as 
these,  the  laboratory  work  furnishes  large  opportunity  for  the  exer- 
cise and  development  of  all-round  "  common  sense." 

19.  Mathematical  Forms.  —  The  use  of  inadmissible  mathemat- 
ical forms  should  be  carefully  avoided.     Perhaps  the  most  com- 
mon error  of  this  sort  is  illustrated  in  the  supposed  equation  :  — 

5  X  8  x  10  =  400 -i- 500  =  .8. 

This  asserts  that  400-7-  500  =  .8,  which  is  true ;  also  that  5  X  8  X 
10  =  400-7-  500,  or  .8,  which  is  absurd.  It  is  evident,  of  course, 
that  this  is  not  the  meaning  intended ;  but  no  other  interpreta- 
tion can  be  given  the  supposed  equation  in  accordance  with  estab- 

<  lished  mathematical  usage,  and  no  departure  from  this  usage  can 

'  be  tolerated. 


MEASUREMENTS  IQ 

MEASUREMENTS 

20.  Measurement  of  Length.  —  The  customary  unit  of  length 
in  scientific  work  is  the  centimeter ;   and  all  lengths  are  to  be 
recorded  in  this  unit  unless  otherwise  specified.     Millimeters  are 
recorded  as  tenths  of  a  centimeter. 

Fractions  of  a  millimeter  are  esti- 
mated in  tenths  and  recorded  as 
hundredths  of  a  centimeter.  Thus 
the  length  of  the  block  illustrated 
in  Figure  i  is  2.35  cm.  The  figure 
also  shows  the  correct  position  of  a 
meter  rod  in  measuring.  If  the  rod  FlG 

were  turned  flat,  the  scale  would  be 

at  a  distance  and  the  measurement  would  be  less  accurate.  It 
is  best  not  to  use  the  end  of  the  rod,  especially  if  it  is  worn. 
Begin  at  some  even  centimeter  or,  better  still,  even  decimeter. 

21.  Order  of  trying  Weights  in  Weighing.  —  Without  system  in 
the  use  of  weights  much  time  is  wasted  in  the  process  of  weighing. 
A  full  set  of  weights,  such  as  is  always  provided  in  the  laboratory, 
includes  all  that  are  necessary  to  balance  any  mass  from  one  equal 
to  the  sum  of  all  the  weights  of  the  set  down  to  one  as  light  as  the 
smallest  of  the  set.     But  a  single  set  is  adequate  only  when  the 
weights  are  tried  in  proper  order. 

Begin  by  trying  the  weight  which  you  estimate  to  be  most 
nearly  equal  to  the  mass  to  be  balanced.  If  it  seems  to  be  nearly 
sufficient,  add  the  next  smaller ;  but  if  it  is  evidently  much  too 
light,  remove  it  and  try  the  next  larger.  Proceed  thus  backward, 
trying  the  larger  weights  till  you  find  that  the  next  larger,  used 
alone,  is  too  large.  The  secret  of  rapid  weighing  is  to  try  out  the 
larger  weights  first.  If  the  process  is  begun  with  too  small  a 
weight,  this  is  commonly  not  discovered  till  all  the  smaller 
weights  have  been  added,  when  the  whole  process  must  be 
repeated,  whereas  it  would  have  been  discovered  by  trying  the 
single  larger  weight. 


20  GENERAL   DIRECTIONS 

Having  thus  determined  the  largest  weight  to  be  used,  add  the 
smaller  weights  in  succession.  If  any  weight  proves  to  be  too 
great  an  addition,  remove  //  (not  a  larger  one)  and  try  the  next 
smaller.  Continue  thus  till  you  come  to  the  smallest  weight 
provided. 

22.  Use  of  the  Platform  Balance.  — The  platform  balance  (Fig. 
2)  is  provided  with  a  graduated  beam,  which  is  to  be  used  instead 

of  weights  smaller  than 
the  maximum  reading  of 
the  beam  (usually  5  g.). 
The  platforms  are  evenly 
balanced  (with  nothing 
on  them)  when  the 
weight  that  slides  on 
the  beam  is  at  the  zero 
FIG-  2'  end  of  the  beam.  As 

the  weight  is  moved  from  this  position,  it  makes  the  side  toward 
which  it  is  moved  heavier,  and  the  platform  on  that  side  descends. 
The  object  to  be  weighed  must  therefore  be  placed  on  the  other 
platform,  i.e.  the  one  at  the  zero  end  of  the  beam. 

In  weighing  proceed  as  follows  :  Place  the  article  to  be  weighed 
on  the  proper  platform.  Slide  the  weight  on  the  beam  to  the  zero 
end.  The  beam  adjustment  is  to  be  held  in  reserve  till  the  weigh- 
ing has  been  brought  within  the  limit  of  the  beam  reading.  When 
this  has  been  accomplished,  make  the  final  adjustment  with  the 
beam.  You  can  save  time  by  steadying  the  platforms  with  the 
hands.  Do  not  waste  time  waiting  for  the  oscillations  to  cease 
entirely.  Some  platform  balances  are  provided  with  a  vertical 
pointer  between  the  platforms.  If  the  oscillations  are  small  and 
this  pointer  moves  to  approximately  equal  distances  on  both  sides 
of  the  zero  point  of  the  graduated  arc  behind  it,  the  weighing  is 
sufficiently  exact.  The  weight  of  the  object  is  the  sum  of  the 
weights  used  plus  the  beam  reading.  This  balance  is  hardly  sen- 
sitive to  less  than  .1  g.,  and  readings  to  this  fraction  are  sufficient. 


MEASUREMENTS 


21 


FIG.  3. 


23.  Use  of  the  Specific  Gravity  or  Beam  Balance.  —  The  beam 
of  this  balance   (Fig.  3)   is  not  fastened  to  the  upright,  and  is 
easily  thrown  out  of  place  in  putting  heavy  objects  on  or  remov- 
ing them  from  the  pans.     To  avoid 

this,  always  support  the  pan  on  the 
heavier  side  by  placing  a  hand 
under  it.  When  balance  is  nearly 
secured,  time  can  be  saved  by 
steadying  the  pans  with  the  hands. 
Watch  the  vertical  pointer  carried 
by  the  beam,  and  adjust  the  weights 
according  to  its  indication.  The 
weighing  is  sufficiently  exact  when 
the  distances  to  which  the  pointer 
swings  on  each  side  of  the  zero  dif- 
fer by  less  than  one  division  of  the  -scale  behind  it.  With  this 
balance  weight  can  be  determined  to  the  nearest  centigram. 

24.  Precautions  to  be  observed  in  Weighing.  —  (i)   Weights, 
especially  heavy  ones,  should  be  placed  near  the  center  of  the 
platform  or  pan. 

(2)  It  is  better  to  handle  weights  with  forceps  than  with  the 
fingers.     If  forceps  are  provided,  use  them.     You  will  find  them 
more  convenient  than  the  fingers,  especially  in  handling  the  frac- 
tional weights. 

(3)  Always  return  weights  to  the  proper  places  in  the  block  as 
soon  as  you  have  finished  weighing.     The  most  convenient  method 
of  counting  weights  is  to  add  them  up  as  they  are  returned  to  the 
block,  beginning  with  the  largest  and  taking  them  in  the  order  of 
their   size.     The   weights   should  never   be  put  down  anywhere 
except  on  the  balance  and  in  their  proper  places  in  the  block. 
If  one  of  the  weights  is  lost,  the  whole  set  is  practically  useless. 

(4)  When  fractional  weights  are  provided,  they  should  consist 
of  the  following  :   .5,  .2,  .1,  .1,  .05,  .02,  .02,  and  .01  g.     If  any  are 
missing,  report  the  fact  to  the  instructor. 


22  GENERAL   DIRECTIONS 

(5)  Before  using  a  balance  observe  whether  the  beam  swings 
freely  and  comes  to  rest  in  a  horizontal  position.     If  it  does  not, 
a  bearing  is  probably  out  of  adjustment. 

(6)  In  weighing  liquids,  see  that  the  outside  of  the  vessel  is 
dry  before  placing    it  on  the   balance.     If  any  liquid  is  spilled, 
wipe  it  up  at  once. 

25.  The  Estimation  of  Tenths.  —  All  laboratory  measurements 
should  be  as  accurate  as  is  possible  with  the  apparatus  provided. 
In  reading  a  scale  of  any  sort,  —  as  the  position  of  a  point  on  a 
meter  rod,  the  position  of  the  pointer  on  the  scale  of  a  spring 
balance,  the  height  of  the  mercury  in  a  thermometer,  etc.,  —  the 
scale  should  be  read  to  tenths  of  its  smallest  division.     Even  if  the 
pupil  has  not  the  skill  to  do  this  accurately,  the  estimate  will  be 
considerably  more  accurate  than  the  nearest  whole  division ;  and 
it  is  the  universal  rule  that  no  error  should  be  unnecessarily  intro- 
duced into  the  work. 

26.  Text-book   References.  —  The   text-books   referred   to   by 
paragraph  numbers  at  the  beginning  of  each  exercise  are  named 
below.     The  references  are  limited  to  the  subject-matter  of  the 
experiments,  their  purpose  being  to  indicate  the  reading  that  may 
profitably  precede  and  accompany  the  laboratory  work,  without 
entering  upon  the  equally  wide  range  of  topics  which  fall  within 
the  scope  of  the  recitation. 

Adams.     Physics  for  Secondary  Schools.      Adams. 

American  Book  Company. 
Coleman.     Elements  of  Physics.     Coleman. 

D.  C.  Heath  and  Company. 
Car.  &  C.     High  School  Physics.     Carhart  and  Chute. 

(Edition  of  1907.)     Allyn  and  Bacon. 
Ches.  G.  &  T.     Physics.     Cheston,  Gibson  and  Timmerman. 

D.  C.  Heath  and  Company. 
Hoad.  Br.     A  Brief  Course  in  Physics.     Hoadley. 

American  Book  Company. 


MEASUREMENTS  23 

Hoad.  El.     Elements  of  Physics.     Hoadley. 

American  Book  Company. 
Mumper.     A  Text-book  in  Physics.     Mumper. 

American  Book  Company. 
Mil.  &  G.     First  Course  in  Physics.     Millikan  and  Gale. 

Ginn  and  Company. 
Went.  &  H.     A  Text-book  of  Physics,  Revised. 

Wentworth  and  Hill.     Ginn  and  Company. 
Jackson.     Elementary  Electricity  and  Magnetism. 

,  Jackson  and  Jackson.     Macmillan  Company. 


II.    DENSITY 


EXERCISE    i.     DENSITY   OF   SOLIDS 

References.  —  Adams,  1-16;  Coleman,  13-20;  Car.  &  C., 
7-10,  140;  Ches.  G.  &T.,  4-8,  15-17,  19-20;  Hoad.  Br.,  13-15, 
145;  Hoad.  EL,  12-16,  156;  Mumper,  7-9,  16-1 8;  Mil.  &  G., 
12-18;  Went.&  H.,  11-15. 

Experiment  i.  —  To  find  the  mass  of  one  cubic  centimeter  of  a 
rectangular  solid. *  « 

Apparatus.  —  A  rectangular  solid,  several  centimeters  in  each 
dimension ;  platform  balance  and  weights ;  forceps  for  handling 
weights  ;  metric  rule  (preferably  a  3O-cm.  rule  with  beveled  edge). 

Experimental  Work.  —  Find  the  dimensions  of  the  solid  in 
centimeters  and  its  weight  in  grams.  Since  the  solid  may  not  be 
perfectly  rectangular  (and  very  probably  is  not),  four  measure- 
ments of  each  dimension  are  to  be  taken,  one  near  each  of  the 
four  edges  extending  in  the  direction  of  the  length,  and  similarly 
for  the  width  and  thickness.  Record  the  four  measurements  of 
each  dimension  even  if  they  are  all  equal.  (Why?)  In  weighing 
the  solid  be  sure  to  place  it  on  the  proper  platform. 

Data  and  Computations.  —  Compute  the  volume  of  the  body 
from  its  average  length,  width,  and  thickness  ;  then  compute  its 
density.  Record  measurements  and  computations  as  follows  :  — 

DIMENSIONS    OF   THE    SOLID 


LENGTH 

WIDTH 

THICKNESS 

—  cm. 

—  cm. 

—  cm. 

—  cm. 

—  cm. 

—  cm. 

—  cm. 

—  cm. 

—  cm. 

—  cm. 

—  cm. 

—  cm. 

Av.         —  cm. 

—  cm. 

—  cm. 

1  Use  the  name  of  the  substance  instead  of  the  word  "  solid." 
24 


DENSITY  OF  SOLIDS 


Weight  of  the  solid 
Volume  of  the  solid  =  ( 
Density  of  the  solid 


—  —  c.c. 

=  —  g.  per  c.c. 


IG' 


Experiment  2. —  To  find  the  density  of  an  irregular  solid  that 
sinks  in  water. 

Apparatus.  —  Platform    balance    and    weights ;     overflow    can 
(Fig.  4)  ;    tumbler ;    vessel  of  water ;  cubic 
centimeter  graduate ;    irregular  solid *  with 
string  tied  to  it ;  mop  cloth. 

[The  copper  boiler  used  in  several  of  the 
heat  experiments  serves  very  well  for  an 
overflow  can,  if  a  short  piece  of  rubber  tub- 
ing is  attached  to  the  spout.  A  cubic  centi- 
meter graduate  having  a  capacity  of  100  c.c. 
and  graduated  in  single  cubic  centimeters  is 
recommended  as  most  serviceable  for  laboratory  work.] 

Experimental   Work. — Weigh   the    solid   before  putting  it  in 
water;  then  find  its  volume  by  measuring  the  volume  of  water 

that  it  displaces  when 
immersed.  If  the  spout 
of  the  overflow  can  is 
not  high  enough  to  allow 
the  graduate  to  be  placed 

under  it,  set  the  can  near  the  edge  of  the  table 
with  the  spout  projecting  over  the  edge.  Fill 
the  can  till  the  water  begins  to  run  out  of  the 
spout,  with  the  graduate  under  the  spout  to  catch 


FIG.  5. 


the  overflow ;  then  empty  the  graduate  and  again  hold  it  under 
the  spout,  as  you  lower  the  solid  into  the  can  by  means  of  the 
string.  In  measuring  the  overflow,  hold  the  eye  on  a  level  with 
the  surface  of  the  water  (Fig.  5),  and  read  the  scale  at  the  level 
of  the  lowest  part  of  the  surface  (seen  through  the  elevated  ridge 

1  Substitute  in  your  record  the  name  of  the  solid  used. 


26  DENSITY 

of  water  at  the  edge).     In  taking  the  reading  estimate  to  tenths 
of  the  smallest  division. 

Data  and  Computations.  —  Record  each  item  on  a  separate 
line,  as  in  the  first  experiment,  and  compute  the  density  of  the 
solid.  If  its  density  is  given  in  Table  I  of  the  Appendix,  compute 
the  percentage  of  error  of  your  result  (Art.  16). 

EXERCISE    2.     DENSITY   OF    LIQUIDS 
References.  —  The  same  as  for  Exercise  i. 

Experiment  3. —  To  find  the  density  of  water  at  the  temperature 
of  the  laboratory. 

Apparatus.  —  Beam  balance  and  set  of  weights  to  i  eg.  (or 
platform  balance  and  weights  to  5  g.)  ;  forceps;  beaker;  loo-c.c. 
graduate ;  mop  cloth. 

Experimental  Work.  —  A  measured  volume  of  water  is  to  be 
weighed  in  the  beaker.  Measure  in  the  graduate  between  90  and 
100  c.c.  of  water  (Fig.  5).  In  reading  the  volume  it  is  necessary 
to  have  the  graduate  exactly  vertical,  and  to  be  sure  of  this  it 
should  stand  on  the  table.  Read  accurately  to  the  nearest  tenth 
of  a  cubic  centimeter.  (An  error  of  one  tenth  of  a  cubic  centi- 
meter affects  the  result  as  much  as  an  error  of  a  decigram  in 
weighing). 

Weigh  in  the  beaker  the  measured  volume  of  water.  Be  careful 
to  empty  the  graduate  to  the  last  drop.  (There  are  only  about  ten 
drops  of  water  in  a  cubic  centimeter.)  Weigh  the  beaker  empty 
and  dry. 

Data  and  Computations.  —  Compute  the  density  of  the  water. 
The  true  density  of  pure  water  at  20°  C.  (which  is  about  the  usual 
temperature  of  the  laboratory)  is  .998  g.  per  cubic  centimeter. 
Compute  the  percentage  of  error  of  your  result.  If  this  is  over  i  %, 
repeat  the  experiment.  (A  large  error  is  almost  certainly  due  to 
an  inaccurate  reading  of  the  volume.  Why  ?)  Record  as  follows  :  — 


DENSITY   OF   LIQUIDS  2/ 

Volume  of  water  used  =    —  cc. 

Weight  of  beaker  and  water 

Weight  of  beaker  empty 

Weight  of  the  water  =()—() 

Computed  density  of  water  =  (     )  -5-  (     ) 

True  value  of  density  (at  20°  C.) 

Error  =()>() 

Percentage  of  error        =(     )  -5-  (     )  x  100  % 

Experiment  4.  —  To  find  the  capacity  of  a  bottle,  making  use  of 
the  known  density  of  water. 

Apparatus  (for  Experiments  4  and  5).  — Beam  balance  and  set 
of  weights  to  i  eg.  (or  platform  balance  and  weights  to  5  g.); 
bottle  of  about  2  oz.  capacity,  with  glass  stopper ;  supply  of  pure 
water;  supply  bottle  of  some  liquid  (saturated  solution  of  zinc 
sulphate  or  table  salt,  alcohol,  or  mercury)  ;  a  jar  of  water  for 
rinsing  j  mop  cloth. 

Experimental  Work.  —  Weigh  the  bottle  empty  with  the  stopper. 
Fill  it  with  pure  water  (not  from  the  jar  for  rinsing)  and  insert  the 
stopper,  being  careful  to  avoid  a  bubble  of  air  under  the  stopper. 
Wipe  the  outside  of  the  bottle  dry  and  weigh.  Return  the  water 
to  the  supply  vessel,  and  stand  the  bottle  on  the  table  inverted  to 
drain.  . 

Data  and  Computations.  —  Compute  the  weight  of  water  that 
the  bottle  holds.  What  is  the  capacity  of  the  bottle  in  cubic 
centimeters,  assuming  the  density  of  water  to  be  i  g.  per  cubic 
centimeter?  Record  each  item  on  a  separate  line,  as  in  the  pre- 
ceding experiment. 

Experiment  5. —  To  find  the  density  of  a  liquid?  using  a  bottle 
of  known  capacity. 

Experimental  Work.  —  Fill   the  bottle   used  in  the  preceding 
experiment  with  the  liquid  provided,  exercising  the  same  precau- 
tions as  before,  and  weigh.    Return  the  liquid  to  the  supply  bottle, 
1  Substitute  the  name  of  the  liquid  in  your  record. 


28  DENSITY 

rinse  the  bottle  used,  and  leave  it  empty.     Use  the  mop  cloth,  and 
leave  the  table  and  scale  pans  dry. 

Data  and  Computations.  —  Compute  the  weight  of  the  liquid 
contained  in  the  bottle,  and  from  this  and  its  volume  (the  capac- 
ity of  the  bottle)  compute  its  density.  If  its  density  is  given  in 
the  Appendix,  compute  the  percentage  of  error  of  your  result. 

Discussion  (Oral).  —  i.  Why  will  more  accurate  results  be  ob- 
tained in  Experiment  3  by  using  about  as  much  water  as  the 
graduate  will  measure  instead  of  only  a  few  cubic  centimeters  ? 

2.  Do  you  think  it  would  be  more  or  less  accurate  to  find  the 
volume  of  a  liquid  by  the  method  of  Experiments  4  and  5  than 
it  would  be  with  a  graduate,  as  in  Experiment  3  ?  Why? 


III.     MECHANICS    OF    FLUIDS 

EXERCISE    3.     GRAVITY   PRESSURE   IN    LIQUIDS 

References.  — Adams,  157-159, 163, 165-168  ;  Coleman,  21-25  ; 
Car.  &  C.,  123-124,  127-128;  Ches.G.&T.,  47-49;  Hoad.  Br., 
I3It  !34-i37;  Hoad.  EL,  140-141,  143-146,  151;  Mumper, 
26-27,  29-31;  Mil.  &  G.,  57-60;  Went.  &  H.,  63-64,  68. 

Experiment  6.  —  To  study  the  pressure  of  a  liquid  due  to  its 
weight  (gravity  pressure),  with  reference  especially  to  the  change  of 
pressure  with  change  of  depth  below  the  surface. 

Apparatus  (for  Experiments  6  and  7).  —  Battery  jar  containing 
water ;  gas-lamp  chimney  or  student-lamp  chimney,  with  an  end 
ground  to  fit  a  plane  surface  ;  small  square  of  cardboard ;  a  stick 
i  ft.  long;  two  beakers,  one  low  and  wide,  the  other  tall  and 
slender,  of  about  the  same  weight  but  very  unequal  diameters. 

Experimental  Work.  —  a.  Place  the  piece  of  cardboard  over  the 
ground  end  of  the  chimney,  and  lower  this  end  into  the  jar  of  water. 
Hold  the  chimney  loosely  so  that  it  will  not  overturn,  and  let  it 
sink  as  far  as  it  will.  What  keeps  it  from  sinking  to  the  bottom  ? 
Hold  the  chimney  in  this  position,  put  the  stick  down  through  it, 
and  note  the  force  required  to  push  the  cardboard  away  from  the 
bottom.  Is  the  chimney  now  sustained  by  the  water  as  it  was 
when  the  cardboard  was  in  place? 

Repeat  the  above  or  vary  the  experiment  in  any  way  that  may 
occur  to  you,  until  you  have  discovered  all  that  you  can  in  regard 
to  the  way  in  which  the  chimney  is  sustained  in  the  water.  State 
briefly  the  facts  observed  and  your  conclusions  from  them. 

b.  With  the  cardboard  over  the  lower  end  of  the  chimney  as 
before,  push  it  slowly  down  to  the  bottom  of  the  jar,  at  the  same 
time  noting  the  change  in  the  tendency  of  the  chimney  either  to 

29 


30  MECHANICS   OF   FLUIDS 

sink  farther  or  to  rise.  What  relation  do  you  observe  between 
the  force  (pressure)  exerted  by  the  water  and  the  depth  at  which 
the  force  is  exerted?  (Statements  of  definite  or  quantitative  re- 
lations are  not  supported  by  this  experiment  and  the  two  following, 
since  no  measurements  are  made.) 

Experiment  7. —  To  observe  whether  the  total  pressure  varies 
with  the  area  of  the  surface  pressed  upon. 

Experimental  Work.  —  With  the  beakers  empty  and  one  in  each 
hand,  push  them,  bottom  down,  into  the  water  to  equal  depths, 
until  the  water  comes  nearly  to  the  top  of  the  shorter  one.  Note 
which  requires  the  greater  downward  pressure  to  hold  it  in  place. 
Explain. 

Experiment  8.  —  To  observe  the  effect  of  the  density  of  a  liquid 
upon  the  pressure  exerted  by  it  at  a  given  depth. 

Apparatus.  —  Tumbler  containing  mercury  ;  tumbler  of  water ; 
two  wooden  blocks  of  the  same  shape  and  size,  and  small  enough 
to  go  into  the  tumblers ;  piece  of  iron. 

Experimental  Work.  —  a.  Compare  the  weight  of  the  mercury 
and  the  weight  of  the  water  by  lifting  the  tumblers.  (Mercury 
is  13.6  times  as  dense  as  water.)  Float  one  of  the  blocks  on  the 
water  and  the  other  on  the  mercury.  Account  for  the  difference 
in  the  depths  to  which  the  two  blocks  sink. 

b.  Push  the  blocks  down  till  they  are  submerged  in  the  liquids. 
Compare  the  forces  necessary  to  do  this,  and  account  for  their 
difference. 

c.  Put  the  piece  of  iron  into  the  mercury.     What  happens  to 
it  ?     Explain. 

Experiment  9.  To  measure  the  pressure  in  water  at  different 
depths  with  a  pressure  gauge,  or  manometer. 

Apparatus. — Hydrometer  jar  filled  with  water ;  two  manome- 
ters, one  containing  water,  the  other  mercury ;  metric  rule. 

[To  reduce  capillary  action,  the  manometer  tubes  should  have 
an  internal  diameter  of  at  least  one  fourth  inch.] 


GRAVITY   PRESSURE   IN   LIQUIDS 


Experimental  Work.  —  a.  •Lift  the  manometer  containing  water 
out  of  the  jar,  and  compare  the  level  of  the  water  in  the  two 
arms   of  the   bend.       Slowly  lower  the   manometer 
into  the  jar  of  water,  and  observe  the  behavior  of 
the  water  in  the  bend  of  the  tube.     Describe  and 
account  for  its  motion.     How  is  the  pressure  of  the 
water  in  the  jar  transmitted    to   the   water   in   the 
manometer  ? 

b.  With  the  manometer  held  in  a  fixed  position, 
measure  the  difference  of  level,  ab  (Fig.  6),  of  the 
water  in  the  two  arms  of  the  bend,  and  the  differ- 
ence, cd,  between  the  level  of  the  water  in  the  jar 
and  the  water  in  the  lower  end  of  the  manometer. 
Take  two  other  pairs  of  measurements  with  the 
manometer  at  different  depths. 

Copy  Figure  6  in  your  note  book,"  and  record  the 
measurements  as  follows  :  — 


FIG.  6. 


Diff.  of  level  ab 
Diff.  of  level  cd 


IST  POSITION 

cm. 

cm. 


2ND  POSITION 

cm. 

cm. 


3RD  POSITION 

cm. 

cm. 


How  do  the  distances  ab  and  cd  for  any  position  of  the  ma- 
nometer compare?  Account  as  fully  as  possible  for  this  relation. 

c.  Repeat  the  experiment  with  the  mercury  manometer,  taking 
three  sets  of  measurements  as  before.  Divide  cd  by  ab  for  each 
position.  Why  is  this  quotient  approximately  equal  to  the  density 
of  mercury?  Suggest  possible  reasons  why  the  equality  is  not 
exact. 

EXERCISE   4.     BUOYANCY   OF   LIQUIDS 

References.  —  Adams,  183-187;  Coleman,  30-32;  Car.  &  C., 
134-138;  Ches.  G.&T.,  55-57  ;  Hoad.  Br.,  143-144 ;  Hoad.  EL, 
154-155;  Mumper,  40-41  ;  Mil.  &G.,  74-75  ;  Went.  &H.,  72-74. 

Apparatus.  —  Specific  gravity  balance  and  weights  to  i  eg.,  or 
platform  balance  and  weights  to  5  g. ;  for  the  platform  balance  a 


MECHANICS   OF   FLUIDS 


support  as  shown  in  Figure  7  ;  overflow  can  ;  beaker  or  tumbler ; 
jar  of  water ;  jar  of  solution  of  table  salt ;    stone  with  attached 

thread  ;    block    of    wood  ; 

mop  cloth. 

Experiment  10.  To  find 
the  relation  between  the  buoy- 
ant force  exerted  upon  a 
stone  in  water  and  the  weight 
of  the  water  it  displaces. 

Experimental  Work.— 

Weigh  the  stone  and  the 
beaker.  Catch  in  the  beaker 
the  water  displaced  by  the 
stone,  when  lowered  by 
means  of  a  string  into  the 
overflow  can  filled  with 
water  (as  in  Experiment  2). 
Weigh  the  displaced  water. 
Suspend  the  stone  from  the  hook  on  the  under  side  of  the 
higher  scale  pan,  and  let  it  hang  entirely  immersed  in  the  jar  of 
water.  Be  careful  to  keep  it  free  from  the  sides  and  bottom  of 
the  vessel.  (If  a  platform  balance  is  used,  adjust  as  shown  in 
Figure  7.)  Weigh  it  thus.  This  is  called  the  weight  of  the  stone 
in  water.  The  difference  between  this  and  the  weight  of  the  stone 
in  air  is  the  buoyant  force  upon  the  stone.  (Why  ?) 

Weigh  the  stone  again,  entirely  immersed  in  water  as  before,  but 
with  a  greater  or  a  less  depth  of  water  above  it  than  before. 

Data  and  Computations.  —  Record    the    measurements  in    the 
form  indicated  below,  and  compute  the  quantities  required  :  — 

Weight  of  the  stone  —  g. 

Weight  of  the  beaker  =  g. 

Weight  of  beaker  and  displaced  water  =  g. 

Weight  of  stone  in  water  =  g. 

Weight  of  stone  at  a  greater  depth  in  water  =  g. 


FIG.  7. 


GRAVITY   PRESSURE   IN   LIQUIDS  33 

COMPUTATIONS 

Weight  of  water  displaced  by  the  stone  =  g. 

Buoyant  force  upon  the  stone  =  g. 
Percentage    of  difference   between    the   buoyant 

force  and  the  weight  of  the  displaced  water  =  %. 

Discussion.  —  i.  Your  results  should  show  (within  a  small 
error)  a  simple  relation  between  the  weight  of  the  displaced  water 
and  the  buoyant  force  upon  the  stone.  State  the  true  relation. 

2.  What  is  likely  to  be  the  principal  source  of  error  in  the  ex- 
periment ?     Why? 

3.  How  is  the  buoyant  force  affected  by  increase  of  depth  after 
the  stone  is  wholly  immersed?     Why? 

4.  When  the  stone  hangs  suspended  by  the  thread  in  water, 
what  forces  sustain  its  whole  weight  ? 

Experiment  1 1.  —  To  find  what  difference's,  if  any,  result  when  a 
saturated  solution  of  table  salt  is  used  instead  of  water  in  the  pre- 
ceding experiment. 

Experimental  Work.  —  Repeat  the  above  experiment,  with  the 
exception  of  the  second  weighing  in  the  liquid,  using  the  salt 
solution  instead  of  water.  Be  very  careful  not  to  mix  the  water 
and  the  solution,  and  return  each  to  the  proper  supply  vessel. 

Comparisons.  —  i.  State  the  law  of  buoyancy  that  holds  for 
both  liquids. 

2.  In  which  of  the  liquids  is  the  buoyant  force  the  greater  ? 
Why? 

Experiment  12. —  To  find  the  relation  between  the  weight  of  a 
block  of  wood  and  the  weight  of  water  that  it  displaces  when 
floating. 

Experimental  Work.  —  Weigh  the  block  of  wood.  Find  the 
weight  of  water  that  the  block  displaces  when  floating,  using  the 
overflow  can  and  beaker.  Return  all  liquids  to  the  labeled  supply 
vessels. 

COLEMAN'S  NEW  MANUAL  —  3 


34  MECHANICS   OF  FLUIDS 

Data  and  Computations.  —  Record  the  measurements  in  the 
usual  form,  and  find  the  percentage  of  difference  between  the 
weight  of  the  block  and  the  weight  of  the  water  it  displaces. 

What  results  should  you  expect  to  obtain  if  you  floated  the 
block  in  the  salt  solution  ? 


EXERCISE   5.     SPECIFIC   GRAVITY   OF   SOLIDS 

References.  —  Adams,  16,  188-189;  Coleman,  33-35;  Car.  & 
C.,  141-143;  Ches.  G.  &  T.,  58-60;  Hoad.  Br.,  146-147,  149; 
Hoad.  EL,  157-160;  Mumper,  42-45  ;  Mil.  £  G.,  76-77  ;  Went. 
&  H,  75. 

Apparatus.  —  Specific  gravity  balance  and  weights  to  i  eg.,  or  a 
platform  balance  and  support  (Fig.  7),  or  a  25o-g.  spring  balance  ; 
thread ;  tumbler  or  jar  of  water ;  solid  denser  and  one  less  dense 
than  water ;  sinker  \  mop  cloth. 

Experiment  13. —  To  find  the  specific  gravity  of  a  solid  that 
sinks  in  water,  applying  the  principle  of  Archimedes. 

Experimental  Work.  —  Weigh  the  solid  in  air.  Suspend  it  from 
the  hook  on  the  under  side  of  the  higher  scale  pan  by  means  of  a 
thread,  of  such  length  that  the  solid  will  be  entirely  immersed 
when  the  tumbler  (or  jar)  of  water  is  placed  beneath  the  pan. 
In  adjusting  the  height  of  the  solid,  it  may  be  found  convenient 
to  change  the  height  of  the  beam  of  the  balance,  which  can  be 
done  by  means  of  the  adjustable  rod  and  thumbscrew.  (If  a 
platform  balance  is  used,  adjust  it  as  shown  in  Figure  7.)  Air 
bubbles  clinging  to  the  immersed  solid  must  be  removed. 
(Why?)  Weigh  the  solid  in  water. 

Data  and  Computations.  —  Compute  the  specific  gravity  of  the 
solid.  If  the  specific  gravity  of  the  substance  is  given  in  Table  I 
of  the  Appendix,  compute  the  percentage  of  error  of  your  result. 
Record  as  follows,  substituting  the  name  of  the  solid  used  :  — 


SPECIFIC  GRAVITY  OF  SOLIDS  35 

Weight  of  the  solid  in  air  =       g. 

Weight  of  the  solid  in  water  =       g. 

COMPUTATIONS 

Weight  of  an  equal  volume  of  water  =       g. 

Specific  gravity  of  the  solid  = 

True  value  of  its  specific  gravity  = 

Error  = 

Percentage  of  error  =        % 

Experiment  14. —  To  find  the  specific  gravity  of  a  solid  that 
floats  in  water,  making  use  of  a  sinker. 

Method.  —  In  this  case  a  denser  body,  called  a  sinker,  is  at- 
tached to  the  solid  to  keep  it  wholly  immersed  when  weighed  in 
water.  The  buoyant  force  on  the  solid,  when  wholly  immersed, 
is  greater  than  its  weight ;  hence  it  tends  to  rise,  and  so  exerts  a 
lifting  force  on  the  sinker.  The  two  together,  therefore,  weigh 
less  in  water  than  the  sinker  alone. 

Experimental  Work.  —  Weigh  the  solid  in  air,  the  sinker  in 
water,  and  both  together  in  water.  Be  careful  not  to  leave  air 
bubbles  clinging  to  either  immersed  body. 

Data  and  Computations.  —  Record  as  follows  :  — 

Weight  of  the  solid  in  air  =       g. 

Weight  of  the  sinker  in  water  =       g. 

Weight  of  the  solid  and  sinker  together  in  water  =       g. 

COMPUTATIONS 

Amount  by  which  buoyancy  upon  the  solid  exceeds 

its  weight  =  g. 

Buoyant  force  upon  the  solid,  or  weight  of  an  equal 

volume  of  water  .  =  g. 

Specific  gravity  of  the  solid  g. 

True  value  of  its  specific  gravity  =        g. 

Percentage  of  error  =        % 


36  MECHANICS   OF   FLUIDS 

EXERCISE    6.     SPECIFIC    GRAVITY   OF   LIQUIDS1 

References.  —  Adams,  190;  Coleman,  36;  Car.  &  C.,  144; 
Ches.  G.  &  T.,  61  ;  Hoad.  Br.,  150;  Hoad.  EL,  161  ;  Mumper, 
46-47;  Mil.  &  G.,  78-80;  Went.  &  H.,  75. 

Experiment  15. —  To  find  the  specific  gravity  of  a  liquid  by 
weighing  a  solid  in  it  and  in  water. 

NOTE.  In  Exercise  4  a  stone  was  weighed  in  water  and  in  a  saturated 
solution  of  table  salt.  This  gives  the  necessary  data  for  computing  the 
specific  gravity  of  the  salt  solution,  and  hence  can  be  made  to  serve  as  the 
experimental  work  required  in  this  experiment. 

Apparatus.  —  Specific  gravity  balance  or  platform  balance  and 
support  (Fig.  7) ;  weights ;  tumbler  of  water ;  tumbler  of  the 
liquid  whose  specific  gravity  is  to  be  found ;  a  solid  denser 
than  water  or  the  liquid,  and  insoluble  in  both  (a  glass  stopper 
serves  well)  ;  mop  cloth. 

Method.  —  By  applying  the  principle  of  Archimedes,  we  find 
the  weight  of  the  liquid  displaced  by  the  solid  when  immersed  in 
it  and  the  weight  of  water  displaced  by  the  same  solid.  These 
are  weights  of  equal  volumes  of  the  liquid  and  water.  (Why?) 
Hence,  dividing  the  one  by  the  other,  we  have  the  specific  gravity 
of  the  liquid. 

Experimental  Work.  —  Weigh  the  solid  in  air,  then  in  the  liquid 
whose  specific  gravity  is  to  be  found.  Wipe  it  dry,  then  weigh  it 
in  water. 

Data  and  Computations.  —  Substitute  in  your  record  the  name 
of  the  solid  and  the  liquid  used  in  the  experiment. 

Weight  of  the  solid  in  air  =       g. 

Weight  of  the  solid  in  the  liquid  =       g. 

Weight  of  the  solid  in  water  =       g. 

1  It  is  not  expected  that  the  pupils  will  perform  the  four  experiments  of 
this  exercise  in  one  laboratory  period.  The  teacher  may  select  from  them 
material  for  one  laboratory  exercise,  or  devote  two  periods  to  the  four  experi- 
ments. 


SPECIFIC   GRAVITY   OF   LIQUIDS 


-m 


COMPUTATIONS 

Weight  of  a  volume  of  the  liquid  equal 

to  the  volume  of  the  solid  =  g. 

Weight  of  an  equal  volume  of  water  =  g. 

Specific  gravity  of  the  liquid  —  g. 

Experiment  16.      To  find  the  specific  gravity  of  a  liquid  by  bal- 
ancing columns. 

Apparatus.  —  One  or  more  U-tubes,  each  containing  water  and 
another  liquid  that  will  not  mix  with  water  (Fig.  8)  ;  meter  stick, 
or  metric  scale,  attached  to  the  support  of  the 
tube. 

Method.  —  Figure  8  represents  a  tube  con- 
taining kerosene,  ab,  and  water,  bnm,  extend- 
ing from  b  round  the  bend  to  m.  The  column 
of  water  below  b  on  the  one  side  exactly 
balances  the  water  up  to  the  same  level,  n,  on 
the  other  side ;  hence  the  column  of  kerosene 
ab  balances  the  column  of  water  mn.  In  other 
words,  these  columns  cause  equal  pressures  at 
b  and  n  respectively. 

Let  d  denote  the  density  of  water,  d*  the 
density  of  the  kerosene,  h  the  height  of  the 
water  column  mn,  and  ti  the  height  of  the  kero- 
sene column  ab.  Then  the  pressure  at  b  is  d*h'  and  the  pressure 
at  n  is  dh.  (How  do  we  know  this  ?)  These  pressures  are  equal, 
as  stated  above,  i.e. 

d*ti  =  dh ; 

from  which  —  =  —  • 

d      h1 

By  definition,  the  specific  gravity  of  the  kerosene  is  -—.     In  the 

experiment  the  lengths  of  the  columns  h  and  h1  are  measured; 
and  the  above  equation  shows  that  the  ratio  of  one  to  the  other 
(of  which  to  which?)  gives  the  specific  gravity  of  the  kerosene. 


b  — 


— -n 


FIG.  8. 


MECHANICS   OF   FLUIDS 


Experimental  Work.  —  Find  by  the  above  method  the  specific 
gravities  of  the  different  liquids  provided.  The  measurements  to 
be  taken  are  the  heights  of  the  columns  above  the  level  of  the 
surface  separating  the  liquids.  Make  a  drawing  of  the  U-tube 
and  its  contents  in  your  note  book,  lettering  it  as  in  Figure  8. 

Experiment  17. —  To  find  the  specific  gravity  of  a  liquid  by 
floating  a  wooden  prism  in  it  and  in  water,  and  measuring  the 
displacement. 

Apparatus.  —  Demonstration  hydrometer  (wood  prism  of  i  sq. 
cm.  cross  section  and  graduated  in  centimeters,  or  one  half  inch 
square  and  graduated  in  inches)  ;  hydrometer  jar  containing 
water  and  one  containing  a  saturated  solution  of  table  salt  or  other 
liquid ;  mop  cloth. 

Method.  —  The  same  body  displaces  equal  weights  of  all  liquids 
in  which  it  floats.  (How  do  we  know  ?)  Let  w  denote  the  weight 
of  the  wood  prism,  d  the  density  of  water,  d'  the  density  of  the 
other  liquid,  v  the  volume  of  water  displaced  by  the  prism  when 
floating,  and  v'  the  volume  it  displaces  in  the  other  liquid ;  then 

w  =  z/'//'  =  z*/.  (Why?) 

d!      v 

From  which  —  =  — . 

d      v 

Hence  by  this  method  the  specific  gravity  of  the  liquid  is  the 
ratio  —  •  (The  ratio  of  what  to  what  ?) 

Experimental    Work.  — 

Float  the  prism  in  water 
and  measure  the  depth  to 
which  it  sinks.  If  the 
water  curves  up  at  the  edge 

where  it  comes  in  contact  with  the  prism,  read  the 
scale  while  looking  through  the  water  along  the 
under  side  of  its  surface  (Fig.  9).  Wipe  the  prism 
dry,  and  measure  the  depth  to  which  it  sinks  in 
the  other  liquid.  Remove  the  prism  and  wipe  it. 


FIG.  9. 


SPECIFIC   GRAVITY   OF   LIQUIDS  39 

Data  and  Computations.  —  Compute   the  displaced  volume  of 

each  liquid.  (The  prism,  if  graduated  in  centimeters,  has  a  cross 

section  of  i  sq.  cm. ;  if  graduated  in  inches,  its  cross  section  is 

.5  x  .5  in.)  Record  as  follows  :  — 

Depth  to  which  the  prism  sinks  in  water          =       cm. 
Depth  to  which  the  prism  sinks  in  the  liquid  =        cm. 

COMPUTATIONS 

Volume  of  the  displaced  water  =       cc. 

Volume  of  the  displaced  liquid  =•      cc. 

Specific  gravity  of  the  liquid  = 

True  value  of  the  specific  gravity  = 

Percentage  of  error  =        cf0 

Experiment  18.  —  To  find  the  specific  gravity  of  liquids  by  means 
of  a*  common  hydrometer. 

Apparatus.  —  Hydrometer  jars  containing  water  and  kerosene, 
alcohol,  or  other  liquids ;  two  common  hydrometers,  with  specific 
gravity  scale,  one  for  light  and  one  for  heavy  liquids ;  jar  of  rinse 
water;  mop  cloth. 

Experimental  Work.  —  Study  the  scale  on  either  hydrometer. 
It  is  graduated  so  that  its  reading  at  the  surface  of  any  liquid  in 
which  it  floats  is  the  specific  gravity  of  the  liquid.  Does  the  read- 
ing increase  toward  the  top  or  the  bottom  ?  Why  ?  Find  from 
the  numbered  divisions  the  value  of  ttxe  smallest  interval.  Is  this 
value  the  same  at  all  parts  of  the  scale  ?  Why  does  the  space  be- 
tween the  lines  grow  smaller  toward  the  bottom  ?  Take  the  read- 
ing of  the  hydrometer  in  water,  with  the  eye  in  the  position  shown  in 
Figure  9.  If  this  reading  is  1000,  call  it  i.  Find  the  value  of  the 
smallest  division  on  the  other  hydrometer.  One  of  these  instruments 
is  for  liquids  denser  than  water,  and  the  other  for  liquids  less  dense. 

Find  the  specific  gravities  of  all  the  liquids  provided.  Rinse 
and  wipe  the  hydrometer  before  putting  it  from  one  liquid  into 
another,  and  before  putting  it  away. 


40 


MECHANICS   OF   FLUIDS 


EXERCISE    7.     PRESSURE   OF   GASES 

References.  —  Adams,  170-174;  Coleman,  34-41,  45;  Car.  & 
C.,  145-147;  Ches.  G.  &T.,  66-67,  70,  77;  Hoad.  Br.,  151-160, 
168;  Hoad.  EL,  162-173,  180;  Mumper,  34-38;  Mil.  &  G.,  81- 
87;  Went.&H.,  76-73,  80. 

Experiment  19.  —  To  study  the  transmission  of  pressure  in  fluids 
by  means  of  the  Cartesian  diver. 

Apparatus.  —  An  hydrometer  jar  nearly  full  of 
water,  in  which  is  floated  a  short  glass  tube  with  a 
bulb  blown  at  one  end,  inverted  and  containing  just 
enough  air  to  float  it  (the  water  must  only  partially 
fill  the  tube)  ;  sheet  rubber  tied  air-tight  over  the  jar. 

[A  satisfactory  substitute  for  the  tube  and  bulb  is 
shown  in  Figure  n.  It  consists  of  a  test  tube,  fitted 
with  a  rubber  stopper  through  which  a 
piece  of  quarter-inch  glass  tubing  is  in- 
serted. The  test  tube  is  partly  filled  with 
water,  the  right  amount  being  determined 
by  trial.] 

Experimental  Work.  —  Press  down  on 
the  rubber  cover  of  the  jar  with  the  fingers,  and  increase 
the  pressure  till  the  floating  tube  sinks.  Diminish  the 
pressure  till  the  tube  rises.  Repeat  and  observe  the 
change  of  level  of  the  water  in  the  tube  as  you  vary 
the  pressure  with  the  fingers.  De3cribe  and  account 
for  this  change  of  level.  What  does  it  prove  con- 
cerning the  transmission  of  pressure  by  air  and  water  ? 
Explain  the  sinking  and  rising  of  the  tube.  FIG.  n. 

Experiment  20. —  To  study  the  principle  of  the  barometer. 

Apparatus.  —  A  bottle  with  a  two-hole  rubber  stopper,  fitted 
with  a  glass  .tube  in  one  hole  and  a  round  plug  in  the  other;  jar 
of  water ;  three  tumblers,  one  containing  mercury ;  a  Y-tube,  con- 


FIG.  10. 


PRESSURE   OF   GASES 


nected  with  two  glass  tubes  of  unequal  diameter  and  about  TOO 
cm.  long,  the  free  end  of  the  Y-tube  fitted  with  a  piece  of  rubber 
tubing  and  pinchcock  (Fig.  12)  ;  meter  rod ; 
tall  iron  stand  and  clamp,  or  other  support ; 
mop  cloth. 

Experimental  Work.  —  a.  Fill  the  bottle 
with  water  and  insert  the  stopper.  See  that 
no  air  remains  in  the  bottle.  With  the  glass 
tube  in  one  hole  of  the  stopper  and  the  plug 
tightly  in  the  other,  apply  the  mouth  to  the 
tube  and  try  to  "  draw  "  water  from  the  bottle 
as  you  would  soda  water  through  a  straw. 
State  and  account  for  the  result.  Do  you 
find  any  evidence  that  the  "  suction  "  exerted 
on  the  water  in  the  tube  consists  of  a  pulling 
force  ? 

b.  Remove  the  plug  from  the  second  hole 
of  the  stopper,  and  repeat  the  experiment. 
State  and  account  for  the    result,   avoiding 
the  use  of  such  indefinite  terms  as  "  draw," 
" suck,"  and  "suction." 

c.  Place  the  long  glass  tubes  in  two  tum- 
blers of  water,  as  shown  in  Figure  12  ;  and,  with  the  pinchcock 
open,  apply  the  mouth  to  the  end  of  the  rubber  tube  and  exhaust 
the  air  till  the  water  rises  nearly  to  the  top  of  the  tubes.     Close 
the  pinchcock  and  remove  the  mouth  from  the  tube.     Open  the 
pinchcock.     Describe  and  account  for  all  that  has  taken  place  in 
the  tubes. 

d.  Again  exhaust  the  air  as  before,  and  take  the  following 
measurements,  using  the  stand  and  clamp  to  hold  the  tubes  in 
the  required  positions  :  — 

With  both  tubes  vertical,  measure  the  height  of  the  column  of 
water  in  each,  measuring  from  the  level  of  the  water  in  the 
tumbler. 


FIG.  12. 


42  MECHANICS   OF   FLUIDS 

With  one  tube  slightly  inclined  and  the  other  very  oblique, 
measure  the  length  of  each  column  along  the  tube. 

Without  changing  the  position  of  the  tubes,  measure  the  verti- 
cal height  of  each  column  above  the  level  of  the  water  in  the  tum- 
blers. (It  will  be  most  convenient  to  measure  the  height  of  the 
columns  above  the  table,  and  afterwards  subtract  the  height  of  the 
water  in  the  tumblers,  also  measured  from  the  level  of  the  table.) 
Record  the  measurements  in  tabular  form,  and  make  a  sketch  of 
the  apparatus. 

e.  Open  the  pinchcock  and  let  the  water  run  out  of  the  tubes. 
Substitute  the  tumbler  of  mercury  for  one  of  the  tumblers  of 
water,  exhaust  the  air  from  the  tubes  till  the  water  rises  nearly  to 
the  top  of  its  tube,  and  close  the  pinchcock.  With  the  tubes  ver- 
tical, measure  the  height  of  the  water  and  mercury  columns  above 
the  level  of  the  liquids  in  the  tumblers.  Empty  the  tubes  and 
remove  them  from  the  tumblers. 

Compute  the  ratio  of  the  height  of  the  water  column  to  the 
height  of  the  mercury  column. 

Discussion.  —  i.  What  causes  the  water  to  rise  in  the  tubes 
when  the  air  is  partially  exhausted  ? 

2.  How  would  you  find  in  grams  per  square  centimeter  the  dif- 
ference between  the  pressure  of  the  air  remaining  in  the  tubes  and 
the  pressure  of  the  outside  air  ? 

3.  What  effect  has  the  diameter  of  the  tube  on  the  height  to 
which  the  water  rises  ?     How  would  the  result  be  affected  if  the 
larger  tube  had  a  diameter  of  several  centimeters? 

4.  What  effect  has  the  unequal  inclination  of  the  tubes  on  the 
vertical  height  of  the  water  in  them?     Explain. 

5.  Account  for  the  relative  heights  of  the  water  and  mercury 
columns  in  the  last  part  of  the  experiment. 

6.  Suggest  a  modification  of  the  experiment  by  which  the  tube 
containing   mercury  would   become  a  barometer.     What  further 
modification  would    be  necessary  to  make   the  tube    containing 
water  a  water  barometer? 


BOYLE'S   LAW 


43 


Experiment  21.  —  To  determine  the  degree  of  exhaustion  that 
the  pupil  can  produce  with  his  mouth. 

Apparatus.  —  A  mounted,  open-tube  manometer  containing 
mercury  (Fig.  13),  the  arms  of  which  are  at  least  40  cm.  long;  a 
heavy-walled  piece  of  rubber  tubing  attached 
to  the  manometer,  with  a  short  piece  of  glass 
tubing  at  its  free  end.  Or,  instead  of  the 
preceding,  a  piece  of  glass  tubing  40  to  50 
cm.  long,  with  a  piece  of  rubber  tubing 
attached,  in  the  other  end  of  which  a  short 
piece  of  glass  tubing  is  inserted;  tumbler 
containing  mercury ;  meter  rod. 

Experimental  Work. — Apply  the  mouth  to 
the  rubber  tube,  and  exhaust  the  air  as  fully 
as  possible.  This  may  be  done  in  stages, 
closing  the  tube  between  the  efforts  either 
by  placing  the  tip  of  the  tongue  against  the 
end  of  the  tube  or  by  pinching  the  tube  in 
the  fingers.  Be  very  careful  not  to  draw  the  mercury  up  into  the 
mouth.  Measure,  in  the  most  convenient  way  that  occurs  to  you, 
the  greatest  difference  of  level  of  the  columns  that  you  can  pro- 
duce. (If  the  straight  glass  tube  and  tumbler  of  mercury  are 
provided  instead  of  the  manometer,  hold  the  tube  in  a  vertical 
position,  with  its  lower  end  in  the  mercury,  and  proceed  as  above.) 

Assuming  that  the  atmospheric  pressure  is  76  cm.,  compute  the 
fraction  of  the  whole  pressure  that  you  removed  by  "  suction." 


FIG.  13. 


EXERCISE   8.     BOYLE'S   LAW 

References.  —  Adams,  177-178;  Coleman,  44-47;  Car.  &  C., 
161-163;  Ches.  G.  &  T.,  75-76;  Hoad.  Br.,  166;  Hoad.  EL, 
178  ;  Mumper,  39  ;  Mil.  &  G.,  95  ;  Went.  &  H.,  79. 

Experiment  22.  —  To  find  the  relation  between  the  volume  of  a 
given  mass  of  air  and  the  pressure  exerted  upon  it. 


44 


MECHANICS  OF   FLUIDS 


Apparatus.  —  A  Boyle's  Law  apparatus  with  adjustable  closed 
and  open  tubes  (Fig.  14). 

Method.  —  NOTE.     No  record  is  required  of  the  following  ex- 
perimental study  of  the  method  of  using  the  apparatus.     If  the 
apparatus  has  been  discussed  in  class,  this  ex- 
perimental study  of  it  may  be  omitted. 

Adjust  the  open  and  closed  tubes  so  that  the 
mercury  stands  approximately  at  the  same  level 
in  both.  What  evidence  is  there  that  the  closed 
tube  contains  a  gas  above  the  mercury  ?  It  is 
air.  How  would  the  mercury  stand  in  the  closed 
tube  if  the  air  were  removed? 

From  the  fact  that  the  mercury  stands  at  the 
same  level  in  the  two  arms,  what  do  you  know 
concerning  the  relative  value  of  the  air  pressure 
upon  the  two  mercury  surfaces  ? 

Raise  the  open  tube  20  or  30  cm.,  and  while 
doing  so,  observe,  the  change  of  level  of  the 
mercury  in  the  closed  tube.  Has  the  confined 
air  increased  or  diminished  in  volume  ?  Has 
the  pressure  upon  it  been  increased  or  de- 
creased, and  from  what  cause?  If  we  let  H 
denote  the  height  of  the  barometer  and  d  the 
difference  of  level  of  the  mercury  in  the  two 
arms,  then  (H  +  d)  cm.  of  mercury  measures 
the  pressure  upon  the  confined  air.  Why? 

Lower  the  open  tube  50  cm.  or  more,  while 
watching  the  change  of  level  of  the  mercury  in 


FIG.  14. 


the  closed  tube.  How  is  the  volume  of  the  confined  air  changing? 
Why  is  it  changing?  Again  letting  d  denote  the  difference  of 
level  of  the  mercury  columns,  the  pressure  upon  the  confined 
air  is  now  (H —  d)  cm.  of  mercury.  Why? 

Experimental  Work. — a.   Clamp  the  closed  tube  near  the  bot- 
tom of  the  standard,  and  leave  it  in  this  position  for  the  first  three 


BOYLE'S   LAW 


45 


sets  of  readings.  Adjust  the  open  tube  so  that  the  mercury 
stands  at  exactly  the  same  level  in  both  tubes.  Take  a  set  of 
readings  as  indicated  in  the  tabular  form  below.  "  Reading  of  top 
of  closed  tube"  means  the  reading  of  the  meter  rod  at  the  level 
of  the  top  of  the  air  space  in  the  closed  tube.  If  the  end  of  the 
air  space  is  round,  estimate  the  position  to  which  it  would  extend 
if  it  were  squared  off  without  changing  the  volume.  The  readings 
called  for  will  be  more  accurately  found  by  holding  the  straight 
edge  of  a  piece  of  paper  across  from  the  tube  to  the  meter  rod. 

b.  Raise  the  open  tube  and  clamp  it  at  about  the  middle  of 
the  standard.     Take  a  second  set  of  readings. 

c.  Again  raise  the  open  tube  and  clamp  it  near  the  top.     Take 
a  third  set  of  readings. 

d.  Raise  the  closed  tube  and  clamp  it  with  its  upper  end  near 
the  top  of  the  standard.     Lower  the  open  tube  and  clamp  it  at 
about  the  middle  of  the  standard.     Take  a  set  of  readings. 

e.  Lower  the  open  tube  and  clamp  it  near  the  bottom.     Take 
a  set  of  readings.     Leave  the  tubes  clamped  at  about  the  same 
height,  and  in  such  a  position  that  the  tube  rests  upon  the  base. 

/  Read  the  laboratory  barometer.  This  reading  is  denoted  in 
one  of  the  headings  of  the  tabular  record  by  H. 

Data  and  Computations.  —  Record  as  indicated  below,  and  perr 
form  the  indicated  computations.  Since  the  closed  tube  is  of  uni- 
form bore,  the  volume  of  any  portion  of  it  is  proportional  to  the 
length  of  that  portion ;  hence  the  length  of  the  air  column  may 
be  taken  to  represent  its  volume.  This  is  done  in  the  record, 
where  the  length  of  the  air  column  is  denoted  by  V. 


SET 

READING  OF 
TOP  OF  CLOSED  TUBE 

READING  OF  TOP  OF  MERCURY  COLUMN 

In  closed  tube 

In  open  tube 

a 
b 
etc. 

crn. 
cm. 

cm. 
cm. 

—  -  —  cm. 
—  -  —  cm. 

/    Height  of  the  barometer,  H  = cm. 


46  MECHANICS   OF  FLUIDS 

COMPUTATIONS 


SET 

LENGTH  OF 
AIR  COLUMN,  OR  V 

DIFFERENCE  OF  LEVEL 
OF  MERCURY  COLS.  =  d 

PRESSURE 
=  H±d=P 

PV 

a 
b 
etc. 

•  cm. 

f    (           \ 

cm.  (of  mer.) 
cm.  (of  mer.) 



cm. 

cm. 

Discussion.  —  i.  According  to  Boyle's  Law,  what  relation  should 
exist  among  the  numbers  of  the  column  headed  PV  (the  product 
of  pressure  and  corresponding  volume)  ? 

2.  Compute  the  percentage  of  difference  between  the  greatest 
and  the  least  of  these  numbers.  With  fair  apparatus  and  reason- 
ably careful  work,  this  difference  will  not  exceed  2  % . 

EXERCISE   9.     THE   SUCTION    PUMP   AND   THE 
SIPHON 

References. — Adams,  179-181;  Coleman,  49,  51,  53;  Car.  & 
C.,  157-160  ;  Ches.  G.  &  T.,  80,  82,  84;  Hoad.  Br..  169-170; 
Hoad.  El.,  182-184,  189;  Mumper,  48-51  ;  Mil.  &  G.,,  99,  102, 
104 ;  Went.  &  H.,  84,  86,  88. 

Experiment  23.  —  To  study  the  action  of  a  suction  pump. 

Apparatus.  —  A  glass  suction  pump  ;  battery  jar  of  water ;  mop 
cloth. 

Experimental  Work.  —  CAUTION.  In  working  the  piston  of  the 
pump,  always  push  and  pull  directly  in  line  with  its  length.  The 
rod  is  easily  broken  with  careless  handling.  Work  the  piston 
slowly,  never  using  more  than  a  moderate  force,  and  be  careful 
not  to  strike  the  pump  against  the  bottom  or  side  of  the  jar. 

Starting  with  the  pump  empty,  place  the  lower  end  in  the  jar  of 
water,  and  work  the  piston  slowly.  Note  when  the  water  begins 
to  rise  in  the  tube  of  the  pump.  What  causes  it  to  rise  ?  (Any 
reference  to  "suction"  explains  nothing.)  Observe  the  behavior 


THE   SUCTION   PUMP   AND   THE   SIPHON  47 

of  the  valves  during  the  downstroke  and  the  upstroke  of  the 
piston.  Operate  the  pump  till  you  understand  the  motion  and 
use  of  the  valves.  To  empty  the  pump,  raise  it  above  the  water, 
pull  the  piston  up,  turn  the  pump  so  that  the  water  above  the 
piston  will  run  out  of  the  spout,  turn  the  lower  end  of  the  pump 
slightly  upward  and  shake  the  lower  valve  out  of  position,  then 
turn  the  lower  end  slightly  downward,  and  the  water  will  run  out. 
Leave  the  pump  empty  and  place  it  on  the  table. 

Draw  two  figures  of  the  pump  —  one  showing  the  position  of  the 
valves  during  the  upstroke  of  the  piston,  the  other  their  position 
during  the  downstroke.  Write  a  brief  description  of  the  action 
of  the  pump,  referring  to  your  drawings  for  illustration. 

Experiment  24.  —  To  study  the  action  of  a  siphon. 

Apparatus.  —  Siphon  made  of  glass  tubing  of  not  less  than  \  in. 
bore,  with  arms  of  unequal  length  and  at  an  angle  of  about  50°  to 
each  other ;  two  battery  jars  with  water,  or  better,  one  jar  and 
sink  at  which  to  work ;  small  beaker ;  mop  cloth. 

Experimental  Work.  —  a.  Invert  the  siphon  and  fill  it  from  the 
beaker  by  pouring  into  one  arm  and  closing  the  end  of  the  other 
arm  with  a  finger,  after  it  is  filled.  When  both  arms  are  full,  stop 
each  end  with  a  finger,  and  turn  the  siphon  right  side  up  (i.e. 
with  the  bend  at  the  top) .  Observe  the  effect  of  removing  the 
finger  from  either  end,  leaving  the  other  end  closed.  State  and 
account  for  the  result. 

b.  Hold  the  ends  of  the  siphon  over  the  jars,  with  the  end  of 
the  longer  arm  lower  than  the  other,  and  remove  the  fingers  from 
both  ends.     From  which  end  does  the  water  run  ?     Repeat  with 
the  end  of  the  shorter  arm  lower  than  the  other.     Does  the  water 
always  run  out  of  the  longer  arm  ?     Does  it  always  run  out  of  the 
lower  end,  whichever  that  may  be  ?     Repeat  till  you  are  sure  of 
the  answer. 

c.  Place  one  of  the  jars,  with  water  in  it,  on  some  support 
above  the  other  jar.     Siphon  the  water  from  this  jar  into  the  lower 
one.     While  the  siphon  is  running,  note  the  effect  of  tilting  it  so 


48  MECHANICS  OF   FLUIDS 

as  to  vary  the  height  of  the  outer  end.  Try  the  effect  of  slowly 
raising  the  outer  end  up  to  and  above  the  level  of  the  surface  of 
the  water. 

Discussion.  —  i.   What  determines  from  which  end  of  the  siphon 
the  water  will  run  ?     Why  ? 

2.  Is  the  rate  of  flow  more  or  less  rapid  when  the  outer  arm  of 
the  siphon  is  lowered  ?     Why  ? 

3.  Why  does  the  water  not  part  at  the  top  and  fall  from  both 
ends  when  a  siphon  is  started? 


IV.     STATICS    OF   SOLIDS 

EXERCISE    10.     EQUILIBRIUM   OF   CONCURRENT 
FORCES 


References.  —  Adams,  47-54;  Coleman,  57-65  ;  Car.  &  C., 40- 
44 ;  Ches.  G.  &  T.,  103-106  ;  Hoad.  Br.,  47,  49  ;  Hoad.  EL,  54, 
56;  Mumper,  58-60,  64,  67;  Mil.  &  G.,  23-26;  Went.  &  H., 

4i-45- 

Experiment  25.  — To  study  the  conditions  for  equilibrium  of  three 
concurrent  forces. 

Apparatus. — Three  2OOo-g.  spring  balances,  with  flat  backs  or 
provided  with  some  simple  support  to  keep  them  level  when  lying 
on   the   table;    three   short 
cords  tied  to  a  small  ring; 
rule ;   a  broad  board,  with 
narrow   strips   on    two    ad- 
jacent sides,  in   which   are 
holes   i   in.  apart,  together 
with  two  nails  and  a  clamp 
(Fig.  15). 

[Where  clamps  can  be 
attached  ,  to  both  sides  of 
the  table  (Fig.  16),  three 
clamps  and  three  blocks 
with  hooks  can  be  used 
instead  of  the  board.  With 


three  tension  clamps   (Fig. 
17)  the  blocks  with  hooks  are  unnecessary.] 
COLEMAN'S  NEW  MANUAL — 4     49 


FIG.  15. 


STATICS   OF   SOLIDS 


FIRST  CASE  :     Wlien  none  of  the  angles  between  the  directions  of 
the  forces  are  specified. 

Experimental  Work. — If  the  board  shown  in  Figure  15  is  pro- 
vided, fasten  two  of  the  balances  by  their  rings  to  nails  inserted 


FIG.  16. 

in  holes  in  the  board,  and  clamp  the  third  balance  in  position, 
passing  the  screw  of  the  clamp  through  the  ring  of  the  balance. 
If  three  clamps  and  three  blocks  are  provided,  clamp  the  blocks 
to  the  table,  and  adjust  as  shown  in  Figure  16. 

Attach  the  cords  on  the  ring  to  the  hooks  of  the  balances. 
Fasten  the  balances  in  position  so  that  the  pull  on  each  is  between 
1000  g.  and  2000  g.  The  forces  and  the  angles 
may  all  be  unequal.  See  that  the  balances  lie 
exactly  in  line  with  the  cords.  (Why?)  Place  a 
large  sheet  of  paper  under  the  cords  with  its  center 
under  the  ring.  Hold  the  paper  in  a  fixed  position 
while  you  make  a  small  dot  exactly  at  the  point 
under  the  ring  over  which  the  three  cords  would 
intersect  if  produced  across  the  ring,  and  a  dot 
directly  under  each  of  the  cords  at  a  distance  of  not 
less  than  8  or  10  cm.  from  the  ring.  The  purpose 
of  these  dots  is  to  determine  the  directions  of  the 
cords  with  the  greatest  possible  accuracy.  Have  the  pencil  sharp 
and  make  the  dots  small.  In  locating  a  dot,  the  eyes  must  be  ver- 
tically above  the  cord,  and  the  cord  should  be  very  near  the  paper. 


EQUILIBRIUM   OF   CONCURRENT   FORCES  51 

Without  disturbing  the  balances,  take  the  reading  of  each,  and 
record  the  forces  on  the  sheet  beside  the  corresponding  cords. 
Estimate  the  readings  of  the  scales  to  tenths  of  the  smallest  division. 

Construction. — The  diagram  based  on  the  above  record  maybe 
constructed  on  the  sheet  used  and  transferred  later  to  the  note 
book ;  or  the  record  may  be  transferred  to  the  note  book  at  once 
by  laying  the  sheet  flat  on  a  page  of  the  note  book  and  pricking  a 
pin  point  through  each  of  the  dots. 

The  construction  must  be  an  accurate  record  of  experimental  re- 
sults. It  is  as  follows  :  Draw  lines  through  the  dots  indicating  the 
directions  of  the  three  cords  (and  hence  also  the  directions  of  the 
forces  exerted  upon  the  ring).  Call  the  point  of  intersection  of 
the  lines  O.  Measure  off  on  the  lines  from  O  distances  propor- 
tional to  the  forces,  using  a  scale  that  will  give  a  rather  large 
figure.  A  scale  of  200  g.  to  the  centimeter  is  about  the  best. 
.Record  the  scale  adopted  near  the  diagram.  Construct  a  paral- 
lelogram upon  any  two  of  the  lines  whose  lengths  have  thus  been 
determined,  taking  the  lines  as  sides  of  the  parallelogram.  For 
convenience  the  force  represented  by  the  line  not  used  in  this  con- 
struction will  be  referred  to  as  the  third  force.  Draw  the  diagonal 
of  the  parallelogram  extending  from  O.  Measure  the  length  of 
this  diagonal,  and  find,  from  the  scale  adopted,  the  magnitude  of 
the  force  it  represents. 

Record  beside  each  of  the  four  lines  extending  from  O  its  length 
in  centimeters  and  the  magnitude  of  the  force  it  represents  in 
grams.  Indicate  the  directions  of  the  forces  by  arrowheads. 

Discussion.  —  i.  What  force  is  represented  by  the  diagonal  of 
the  parallelogram? 

2.  How  should  this  line  compare  in  magnitude  and  direction 
with  the  line  representing  the  third  force  ? 

3.  In  what  respects  and  to  what  extent  do  the  relations  shown 
in  your  diagram  differ  from  the  true  relations?     Draw  the  angle 
that  measures  the  error  in  the  direction  of  the  diagonal,  assuming 
the  direction  of  the  third  line  from  O  to  be  correct. 


52  STATICS   OF   SOLIDS 

SECOND  CASE  :  When  the  angle  between  the  directions  of  two 
of  the  forces  is  90°. 

Experimental  Work.  —  Repeat  the  experiment,  with  the  balances 
adjusted  so  that  two  of  them  will  act  at  an  angle  of  exactly  90° 
after  the  forces  are  applied,  none  of  the  forces  being  less  than 
1000  g.  Measure  the  angle  with  a  piece  of  paper  folded  so  that 
the  two  parts  of  a  straight  edge  coincide. 

Construction.  —  Using  the  same  method  as  before,  find  the  re- 
sultant of  the  two  forces  acting  at  an  angle  of  90°.  Record  all 
lengths  and  the  forces  represented  by  them  in  the  diagram. 

Computation  and  Comparison.  —  i.  Find  the  same  resultant  by 
computation.  (The  square  on  the  hypotenuse  of  a  right  tri- 
angle is  equal  to  the  sum  of  the  squares  on  the  other  two  sides.) 
Remember  that  the  resultant  is  a  force,  not  a  line. 

2.   Write  down  for  comparison  :  — 

The  resultant  found  by  construction  =       g. 

The  resultant  found  by  computation  =       g.  • 

The  equilibrant  (reading  of  the  third  balance)      =       g. 

Compute  the  percentage  of  difference  between  the  largest  and 
the  smallest  of  these  quantities.  This  difference  is  due  to  experi- 
mental errors.  What  are  the  probable  sources  of  error? 

EXERCISE  ii.     EQUILIBRIUM  OF  PARALLEL   FORCES 

References.  —  Adams,  55;  Coleman,  67-68;  Car.  &  C.,  46; 
Ches.  G.  &  T.,  90-95  ;  Hoad.  Br.,  51  ;  Hoad.  El.,  60;  Mumper, 
64;  Went.  &H.,  53. 

Experiment  26.  — r  To  study  the  conditions  for  equilibrium  of  three 
pa  r a  lie  I  forces. 

Apparatus.  —  Meter  rod ;  two  20oo-g.  spring  balances ;  two 
unequal  weights  of  about  2000  g.  and  3000  g.,  respectively ;  cord ; 
frame  to  support  the  balances  (Fig.  34)  ;  rule. 


EQUILIBRIUM  OF  PARALLEL  FORCES  53 

Method.  —  The  three  parallel  forces  to  be  studied  act  upon  a 
meter  rod.  Two  of  them  are  exerted  by  spring  balances,  and  the 
other  by  a  weight  (Fig.  18).  The  weight  of  the  rod  itself  is  an 
additional  force  which  necessarily  affects  the  readings  of  the 
balances ;  but  since  this  force  is  not  included  in  the  problem 


FIG.  18. 

under  consideration,  it  is  eliminated  by  subtracting  from  all  read- 
ings of  the  balances  the  forces  exerted  by  the  balances  in  support- 
ing the  rod  alone. 

Experimental  Work.  —  a.  Adjust  the  balances  and  meter  rod  as 
shown  in  Figure  18,  but  without  the  weight  attached.  The  sup- 
porting cords  must  be  vertical.  For  convenience  in  reading  the 
distances,  the  balances  may  be  hung  80  cm.  apart  and  the  cords 
attached  to  the  rod  10  cm.  from  each  end.  Take  the  readings  of 
the  balances  when  supporting  the  rod  only.  Record  the  readings 
as  the  zero  readings  of  the  left  and  right  scales,  respectively. 
These  are  the  forces  necessary  to  support  the  weight  of  the  rod, 
and  they  are  to  be  subtracted  from  all  later  readings  of  the  scales 
in  order  to  obtain  the  forces  necessary  to  balance  the  weight  that 
is  hung  on  the  rod.  In  order  to  keep  the  zero  readings  the  same 
throughout  the  experiment,  the  rod  must  always  be  supported 
from  the  same  points. 


54 


STATICS   OF   SOLIDS 


In  Figure  19,  A  and  B  denote  the  points  of  support  of  the  rod, 
and  C  the  point  where  the  weight  hangs.  In  this  figure,  and  also 
in  the  record,  dl  denotes  the  distance  AC,  d2  the  distance  CB,  W 
the  attached  weight,  and^  and/2  the  forces  necessary  to  balance 

W  (not  including  the  forces 

^  necessary     to     balance    the 

If        weight  of  the  rod). 

b.  Hang  one  of  the  weights 
on  the  rod  midway  between 
the    supporting    cords,   and 
record   the  readings  of  the 
scales    and    the   equal    dis- 
tances d±  and  d>2. 

c.  Move  the  weight  10  cm. 
or  more  to  one  side  of  the 


B 


W 


FIG.  19. 


center,  and  take  a  second  set  of  readings  (i.e.  the  scale  readings 
and  dl  and  d^). 

d.  Take  a  third  set  of  readings,  using  the  other  weight  and 
placing  it  in  a  new  position  on  the  rod.  Remove  the  weight. 

Draw  a  figure  for  each  set  of  readings  taken,  similar  to  Figure 
19,  representing  the  distances  and  the  forces  approximately  to 
scale.  (An  accurate  construction  is  not  required.) 

Data  and  Computations.  —  Record  measurements  and  computa- 
tions as  follows  :  — 


a.    ZERO  READINGS:  Left  Scale  =-  g. 


Right  Scale  = 


SET 

SCALE  READING 

W 

Left 

Right 

b 

g. 

g- 

g- 

cm. 

cm. 

d 

g* 
g- 

g* 
g- 

g- 
g- 

cm. 

cm. 

EQUILIBRIUM   OF   PARALLEL   FORCES 
COMPUTATIONS 


55 


FORCES 

SET 

A+A 

4-^1 

Difference 

%  of  Diff. 

7?     /*-i-  f 

R  -  W 

K  yiT/j 

/, 

/I 

V 

b 

g- 

g- 

— 



o/ 
~  /o 

g- 

g. 

c 

g- 

g- 

— 

— 



o/ 

~~  /o 

g- 

g- 

d 

g- 

g- 

' 





—  °/ 
/o 

g- 

g- 

Discussion. —  i.  The  difference  between  the  ratios^  -r-/2  and 
*/2  -5-  //i  is  due  to  experimental  errors.  It  should  not  exceed  2  % 
unless  the  spring  balances  are  very  inaccurate.  If  the  difference 
exceeds  this,  try  to  discover  the  source  of  the  trouble. 

2.  Write  the  proportion  that  holds  between  the  true  values  of 
the  quantities',^,  d^  4>  and  state  the  proportion  in  words. 

3.  What  relation  holds  between  the  true  values  of  ,/2,  and  Wt 
What  name  applied  to  W  expresses  its  relation  to  the  other  two 
forces? 

ALTERNATIVE   METHOD 

Apparatus.  —  Meter  rod ;  three  2ooo-g.  spring  balances ; 
three  clamps  and  blocks  with  hooks  for  holding  balances  (Fig. 
19),  or  three  tension  clamps;  cord. 

General  Directions.  — 

Follow     the     directions 

given  above,  but  with  the 

following  modifications : 

A  third   spring  balance 

is  used  instead   of   the 

weight,  and  the  rod  and  Jit  T  h 

balances  lie  on  the  table 

(Fig.    20).      The  three 

cords   must  be   parallel, 

and  their  lengths  are  to  FIG.  20, 


50  STATICS   OF   SOLIDS 

be  so  adjusted  that  the  reading  of  the  single  opposing  balance 
is  nearly  2000  g.  No  allowance  is  required  for  the  weight  of  the 
rod,  since  it  is  not  supported  by  any  of  the  balances ;  hence  omit 
the  experimental  work  of  paragraph  (a)  above. 

Before  reading  the  balances,  raise  the  meter  rod  one  or  two 
centimeters,  and  let  it  drop.  Repeat  this  several  times,  so  that  all 
parts  of  the  apparatus  will  come  into  proper  adjustment  without 
hindrance  from  friction.  This  is  very  important.  In  the  dia- 
grams and  the  record  designate  the  outer  forces  as  /x  and  /2  and 
the  inner  force  as  f». 


EXERCISE    12.     MOMENTS   OF   FORCE 

References.  —  Adams,  108-111;  Coleman,  69-71;  Car.  &  C., 
47  a\  Ches.  G.  &  T.,  90-93;  Hoad.  Br.,  96-98;  Hoad.  El., 
106-108  ;  Mumper,  66  ;  Mil.  &  G.,  208-210  ;  Went.  &  H.,  49-51. 

Experiment  27.  —  To  study  the  conditions  for 
equilibrium  of  two  forces  with  respect  to  rotation 
about  an  axis. 


Apparatus.  —  Meter  rod  with  hole  at  50  cm.; 
upright  with  nail  to  support  the  rod  ;  spring  balance ; 
four  weights,  two  of  which  are  equal ;  rule. 

[The  hole  in  the  rod  should  be  exactly  at  50  cm. 
and  slightly  displaced  laterally,  so  that  the  rod  will 
balance  horizontally  with  slight  stability  on  a  nail. 
If  one  end  of  the  rod  is  heavier  than  the  other,  the 
defect  can  be  remedied  by  boring  small  holes  in 
the  heavier  end  or  by  means  of  a  sliding  wire  rider. 
A  i-kg.  weight  should  be  used  with  a  2OOo-g.  balance, 
and  a  loo-g.  weight  with  a  25o-g.  balance.  Either 
combination  will  serve.  A  set  of  "  universal  labora- 
tory weights"  (Fig.  21)  is  very  convenient  for  this 
exercise  and  those  on  machines.  The  set  runs  from 
(C.  H.  Stocking  Co.,  Chicago,  manufacturers.)] 


FIG.  21. 


5  to  1000  g. 


MOMENTS   OF   FORCE  57 

Experimental  Work.  —  a.  Hang  the  meter  rod  on  the  nail. 
Hang  one  of  the  equal  weights  near  each  end  of  the  rod,  and 
adjust  them  so  that  the  rod  balances  in  a  horizontal  position. 
Let  wl  and  w2  denote  the  weights,  and  av  and  <z2  the  respective 
distances  from  their  points  of  suspension  to  the  axis  (the  nail). 
Record  the  values  of  these  quantities  in  tabular  form,  as  given 
below. 

b.  Hang  two  unequal  weights  on  the  rod,  and  adjust   them 
so  that  they  balance.     The  nearer  the  weights  are  to  the  ends  of 
the  rod,  the  more  accurate  the  results  are  likely  to  be.     (Why?) 

c.  Repeat  with  two  other  unequal  weights. 

d.  With  a  25o-g.  spring  balance  use  a  loo-g.  weight  for  the 
remaining  work ;  with  a  2Ooo-g.  balance  use  a  looo-g.  weight,  or 
the  largest  provided.     Hang  the  weight  20  cm.  from  an  end  of 
the  rod,  and  support  the  rod  on  the  hook  of  the  spring  balance, 
applied  nearer  the  same  end  of  the  rod.     Let  f±  denote  the  force 
applied  by  means  of  the  balance  and  a±  the  distance  from  its  point 
of  application  to  the  axis ;    and  let  w2  denote  the  weight  and  a2 
the  distance  of  its  point  of  application  from  the  axis. 

e.  Repeat  with  the  balance   applied  between  the  weight  and 
the  axis.     After  recording  the  set  of  measurements,  try  the  effect 
of  applying  the  balance  nearer  and  nearer  the  axis,  until  it  is  as 
near  as  you  can  get  it.    State 

the  general  result  of  these 

trials  without  taking  meas- 
urements. 

Draw   a   figure   for   each 

set  of   readings,  similar  to  PIG  22 

Figure  22,  representing  the 
distances  and  the  forces  approximately  to  scale. 

/.  Adjust  the  weight  and  the  balance  as  in  either  (//)  or  (e),  with 
the  hook  tied  to  the  rod  to  keep  it  from  slipping,  and  observe  the 
change  in  the  reading  of  the  balance  when  the  force  exerted  by  it 
is  made  more  and  more  oblique  to  the  vertical.  Does  the  moment 
of  the  force  change  as  the  force  changes  ?  How  do  you  know  ? 


STATICS   OF   SOLIDS 


Does  its  arm  change  (while  it  is  still  applied  at  the  same  point)  ? 
What  distance  is  the  arm  of  the  force  when  the  force  is  oblique  ? 
Measurements  need  not  be  taken. 

Data  and  Computations.  —  Record  in  the  form  given  below. 
Compute  the  products  w^  (or  /^i)  and  w2a2  for  each  set  of 
measurements,  also  their  difference  and  percentage  of  difference. 


a 
b 
c 

d 

e 

V>1 

1V2 

«1 

«2 

Wl«i 

W2«2 

DifT. 

%ofDiff. 

g- 
g 
.g- 
/i 
g- 
g- 

—  g- 
—  g- 
—  g- 

—  g- 
—  g. 

cm. 
cm. 
cm. 

cm. 

cm. 

/1«1 





% 

% 

o/ 
/o 

()/ 
~~   fO 

"/ 

—  cm. 
cm. 

cm. 



/(> 

Discussion.  —  i.  Express,  both  as  an  equation  and  as  a  pro- 
portion, the  relation  that  holds  for  the  true  values  of  the 
quantities  wl9  w2,  alt  and  a2 ;  and  also  for  the  true  values  of  w2, 
/!,  aly  and  a2. 

2.  State  the  two  conditions  necessary  for  the  equilibrium  of  two 
forces  with  respect  to  rotation  about  an  axis,  and  word  the  state- 
ment so  as  to  cover  every  case  presented  in  the  experiment. 

3.  In  this  experiment  we  have  not  had  occasion  to  consider 
the  force  exerted  on  the  rod  by  the  nail.     What  do  you  know 
(from  the  laws  studied  in  Exercise  n)  about  the  magnitude  and 
direction  of  this  force  and  its  effect  on  the  behavior  of  the  rod  ? 

4.  Does  the  force  exerted  by  the  nail  tend  to  cause  the  rod  to 
turn  in  either  direction?      Why  or  why  not? 

5.  In  Exercise  n  what  forces  tend  to  cause  rotation  about  C 
as  an  axis?     Why  is  there  not  rotation  about  this  point?     Prove 
your  answer  correct  by  making  use  of  any  one  of  the  sets  of 
measurements  taken  in  that  exercise. 


CENTER   OF  GRAVITY   AND    MOMENT  OF   WEIGHT        59 

EXERCISE    13.     CENTER  OF   GRAVITY  AND  MOMENT 
OF   WEIGHT 

References.  —  Adams,  61-66;  Coleman,  73-75;  Car.  and  C., 
5!-52>  55-56;  Ches.  G.  &  T.,  98-100;  Hoad.  Br.,  70-71,  74; 
Hoad.  EL,  82-86;  Mumper,  68-69;  Mil.  &  G.,  33-34 ;  Went. 
&  H.,  55-59- 

Experiment  28.  —  To  find  whether  the  point  of  application  of  the 
weight  of  a  body,  regarded  as  a  single  force,  changes,  or  remains 
the  same,  under  different  conditions. 

Apparatus.  —  Meter  stick ;  wooden  or  iron  clamp ;  support 
with  a  narrow  edge ;  platform  balance  and  weights. 

FIRST  CASE:    A  REGULAR  BODY 

Experimental  Work.  —  Weigh  the  meter  stick.  Balance  it  in  a 
horizontal  position  on  the  sharp  edge  of  the  support.  The  weight 
of  the  stick,  under  these  conditions,  is  evidently  equivalent  to  a 
single  force  acting  at  a  point  vertically  above  the  support,  for  it  is 
balanced  by  the  upward  pressure  of  the  support.  This  point,  then, 
is,  by  definition,  the  center  of  gravity  of  the  stick  when  thus 
balanced.  Record  its  position  as  the  reading  of  the  meter  scale 
at  the  axis.  (On  account  of  slight  variations  in  the  density  or 
cross  section  of  the  stick,  the  reading  may  not  be  exactly  50  cm.) 

The  purpose  of  the  experiment  is  to  determine  whether  the 
weight  of  the  stick  is  equivalent  to  a  single  force  acting  at  this 
same  point,  or  whether  it 
must  be  regarded  as  act- 
ing  at  some  other  point, 
when  the  stick  is  bal- 
anced in  a  different  way  ;  FJG 
in  other  words,  to  deter- 
mine whether  the  center  of  gravity  remains  fixed  or  shifts  to  a 
new  position  when  the  conditions  are  changed.  Balance  the  stick 
in  a  horizontal  position  on  the  support  as  before,  but  with  a  loo-g. 


60  STATICS   OF   SOLIDS 

weight  hanging  on  it  i  cm.  from  its  zero  end  (Fig.  23).  (It  is 
less  convenient  to  calculate  distances  from  the  loo-cm,  end.) 
Record  the  position  of  the  axis  as  the  reading  of  the  meter  scale 
at  that  point. 

Data  and  Computations.  —  When  the  stick  is  balanced  with  the 
attached  weight,  this  weight  tends  to  pull  the  shorter  end  of  the 
stick  down ;  while  the  weight  of  the  stick  itself  tends  to  pull 
the  longer  end  down.  Obviously,  if  we  regard  the  weight  of  the 
stick  as  one  force,  the  stick  is  in  equilibrium  under  the  action  of 
two  equal  and  opposite  moments  of  force ;  namely,  the  moment 
of  the  attached  weight  and  the  moment  of  the  weight  of  the  stick. 
That  is,  the  product  of  the  attached  weight  and  its  arm  is  equal 
to  the  product  of  the  weight  of  the  stick  and  its  arm  (the  arm  of 
the  weight  of  the  stick  being  the  distance  from  the  axis  to  the 
point  of  application  of  the  weight  of  the  stick,  wherever  that 
may  be). 

Let  Wi  denote  the  attached  weight,  w2  the  weight  of  the  stick, 
#!  the  arm  of  the  attached  weight,  and  a2  the  arm  of  the  weight  of 
the  stick.  Then,  as  stated  above,  w^a^  —  W2w2.  Since  a2  is  the 
only  unknown  quantity  in  this  equation,  it  can  be  computed  ;  and, 
measuring  off  this  distance  from  the  axis,  we  come  to  the  point 
where  the  weight  of  the  whole  stick  must  be  regarded  as  acting  to 
produce  the  observed  effect.  The  point  thus  found  is,  therefore, 
the  center  of  gravity  under  the  conditions  of  the  experiment.  Is 
this  second  position  of  the  center  of  gravity  the  same  as  the 
first? 

Copy  Figure  22  in  your  note  book,  and  record  data  and  com- 
putations as  follows :  — 

Weight  of  the  meter  stick,  w^  =       g. 
Position  of  the  axis  when  the  stick  is  balanced  alone 

(first  position  of  the  center  of  gravity  of  the  stick)  =       cm. 

Attached  weight,  w±  =       g- 

Position  of  attached  weight  =  i  cm. 

Position  of  axis  for  equilibrium  with  weight  attached  =       cm. 


CENTER   OF   GRAVITY  AND   MOMENT   OF   WEIGHT        6 1 

COMPUTATIONS 

Arm  of  attached  weight,  a±  =       cm. 

Arm  of  the  weight  of  the  stick  (distance  from  the  axis 
to  second  position  of  center  of  gravity  of  stick), 
a2  =  w^a^  -r-  w2  =  cm. 

Second  position  of  center  of  gravity  of  stick  =  posi- 
tion of  the  axis  -{-  a2  =  cm. 

Difference  between  the  first  and  second  positions  of 

center  of  gravity  of  stick  =  cm. 

Conclusion.  —  Assuming  that  experimental  errors  may  reason- 
ably account  for  a  difference  of  .3  cm.  in  the  two  positions  found 
for  the  center  of  gravity  of  the  stick,  what  answer  have  you  found 
to  the  question  under  consideration? 

SECOND  CASE:    AN  IRREGULAR  BODY 

General  Directions.  —  Repeat  the  above  experiment  with  a 
clamp  firmly  attached  to  the  loo-cm,  end  of  the  stick,  and 
remaining  thus  throughout  the  experiment.  The  stick  and  clamp 
are  to  be  regarded  as  one  irregular  body.  Weigh  this  irregular 


FIG.  24. 

body,  and  find  its  center  of  gravity  when  balanced  alone  on  the 
axis,  and  again  when  it  is  balanced  with  a  weight  of  200  g.  to 
500  g.  attached  near  the  lighter  end  (Fig.  24).  If  there  is  time 
enough,  make  two  trials,  either  with  different  attached  weights  or 
with  the  weight  in  different  positions. 

Do  the  results  in  this  case  lead  to  the  same  conclusion  as  before, 
or  to  a  different  one  ? 


62  STATICS   OF   SOLIDS 

EXERCISE    14.     CENTER   OF   GRAVITY   AND   THE 
STATES  OF   EQUILIBRIUM 

References.  —  Adams,  61-69;  Coleman,  73-80;  Car.  &  C.s 
51-52,  55-58;  Ches.  G.  &  T.,  98-101;  Hoad.  Br.,  70,  71,  74, 
75;  Hoad.  EL,  82-87;  Mumper,  68-69 ;  Mil.  &  G.,  33-37  ; 
Went.  &  H.,  55-57,  60. 

Experiment  29.  —  To  find  the  center  of  gravity  of  an  irregular 
piece  of  cardboard. 

Apparatus  (for  Experiments  29  and  30).  —  Irregular  piece  of 
cardboard ;  pins ;  small  plumb  line  made  of  thread  and  bullet ; 
rule. 

Experimental  Work. — a.  Stick  a  pin  through  the  cardboard 
near  one  corner,  and  enlarge  the  hole  enough  to  allow  the  card- 
board to  swing  freely.  Stick  the  pin,  with  the  cardboard  on  it, 
horizontally  into  the  edge  of  the  table  or  other  support.  Hang 
the  plumb  line  on  the  pin  in  front  of  the  cardboard,  but  not  quite 
touching  it.  When  both  have  come  to  rest,  grasp  them  together 
at  the  bottom,  make  a  dot  accurately  under  the  thread,  and  with 
a  sharp  pencil  and  rule  draw  a  line  connecting  the  dot  with  the 
point  of  suspension.  How  do  you  know  that  the  center  of  gravity 
of  the  cardboard  is  at  some  point  on  this  line,  or,  more  accurately, 
at  some  point  directly  back  of  this  line,  midway  between  the 
surfaces? 

b.  Suspend  the  cardboard  from  another  corner,  and  determine 
a  second  line  in  the  same  way.     Where  is  the  center  of  gravity  of 
the  body.     Would  this  point  be  vertically  under  any  point  of  sus- 
pension from  which  the  cardboard  hangs  at  rest?     Test  the  mat- 
ter by  suspending  the  body  from  a  third  point,  chosen  at  random. 
State  the  result. 

c.  Trace  the  outline  of  the  cardboard  in  your  note  book,  mark 
the  three  points  of  support,  and  draw  the  plumb  lines.    Letter  the 
center  of  gravity  C. 


CENTER  OF  GRAVITY  AND   STATES  OF   EQUILIBRIUM       63 

Experiment  30.  —  To  study  the  states  of  equilibrium  of  a  sus- 
pended body. 

Experimental  Work.  —  a.  Hang  the  cardboard  again  from  one 
of  the  holes  near  the  edge,  turn  it  out  of  the  position  in  which  it 
hangs  at  rest,  and  release  it.  How  does  it  behave  as  it  comes  to 
rest  ?  Account  for  this  motion  as  definitely  as  you  can.  In  what 
state  of  equilibrium  does  it  come  to  rest?  How  do  you  know? 

b.  Suspend  the  cardboard  exactly  at  the  center  of  gravity,  en- 
large the  hole  till  it  turns  freely,  and  note  its  behavior  when  turned 
out  of  a  position  of  rest  and  released.     Does  it  always  come  to 
rest  in  the  same  position? 

It  is  not  easy  to  find  the  center  of  gravity  exactly ;  it  generally 
happens  that  the  hole  is  far  enough  out  of  position  to  affect  appre- 
ciably the  behavior  of  the  cardboard.  What  reason  have  you,  if 
any,  for  thinking  that  such  is  the  case  in  your  experiment  ?  How 
would  the  body  behave  when  turned  and  released,  if  it  were  sus- 
pended accurately  at  the  center  of  gravity?  Why?  In  what  state 
of  equilibrium  would  it  be  when  thus  suspended  and  at  rest? 

c.  Suspend  the  cardboard  at  one  of  the  outer  holes,  and  try  to 
balance  it  with  the  center  of  gravity  vertically  above  the  support. 
Why  is  it  practically  impossible  to  secure  equilibrium  in  this  posi- 
tion?    What  would  equilibrium  in  this  position  be  called? 

Experiment  31.  —  To  study  the  states  of  equilibrium  of  bodies 
supported  on  a  horizontal  surface. 

Apparatus.  —  Such  bodies  as  cylinder,  cone,  sphere,  oblate  and 
prolate  spheroids  ;  an  empty,  round-bottom  flask ;  a  round-bottom 
flask  loaded  with  shot  so  that  it  will  stand  upright.  (The  shot  can 
be  kept  in  place  by  parafftne  or  wax  melted  over  it.) 

Experimental  Work.  —  a.  A  body  may  be  in  different  states  of 
equilibrium  at  the  same  time  with  respect  to  motion  in  different 
directions.  Experiment  with  the  different  bodies  provided,  and 
determine  their  states  of  equilibrium  in  different  positions,  and 
with  respect  to  motion  in  different  directions  for  each  position. 


STATICS   OF  SOLIDS 


Give  a  complete  account  of  each  case  studied,  with  drawings  to 
illustrate.     Include  cases  of  unstable  equilibrium,  whether  you  can 

perfectly  realize  them  or  not. 
Locate  as  closely  as  possible  the 
center  of  gravity  in  each  draw- 
ing, and  indicate  by  a  dotted  line 
the  path  that  it  would  describe  if 
the  body  were  tipped  or  rolled. 

b.  Balance  your  pencil  on  its 
point  on  your  finger,  making  use 
of  a  pocketknife  to  secure  stable 
equilibrium,  as  shown  in  Figure 
25.  Draw  a  figure  showing  the 
position  of  equilibrium  as  you 
secured  it,  and  indicate  approxi- 
mately the  position  of  the  center 

of  gravity  of  the  knife  and  pencil  regarded  as  one  body.     How 
definitely  does  the  experiment  determine  this  center  of  gravity? 

EXERCISE    15.      STIFFNESS   OF   BEAMS.     THE   TRUSS 

References.  —  Adams,  26,  140-143;  Coleman,  202-204,  2°6 ; 
Car.  &  C.,  14-15  ;  Hoad.  Br.,  27  ;  Hoad.  EL,  27-30  ;  Mil.  &  G., 
152-156  j  Mumper,  22  ;  Went.  &  H.,  23-30. 

Experiment  32.  —  To  study  the  effect  of  the  length  and  the  shape 
of  the  cross  section  of  a  beam  upon  its  stiffness. 

Apparatus.  —  Three  meter  sticks  ;  small  rod  of  steel  or  brass  one 
meter  long,  and  a  tube  of  the  same  material,  length,  and  weight. 

Experimental  Work.  —  a.  Note  the  effort  required  to  bend  a 
meter  stick  in  the  hands,  while  holding  it  near  the  ends.  Repeat 
several  times,  decreasing  the  distance  between  the  hands  with  each 
trial,  and  observe  how  difficult  the  bending  becomes  as  the  length 
of  the  bent  portion  is  decreased.  Account  for  the  observed  facts 
as  fully  as  you  can. 


STIFFNESS  OF   BEAMS.    THE  TRUSS 


b.  Holding  the  rod  at  the  ends,  bend  it  as  before  in  the  plane 
of  its   smallest  dimension    (thickness),  then  in  the  plane  of  its 
width.     Compare  the  stiffness  of  the  rod  with  respect  to  bending 
in  these  two  planes.     (Is  the  stiffness  slightly  greater,  considerably 
greater,  or  several  times  greater  in  the  one  case  than  in  the  other?) 
To  vary  the  experiment,  rest  the  ends  of  the  rod  on  fixed  supports 
(as  the  edges  of  two  stools),  first  flatwise,  then  on  edge;   and, 
grasping  it  firmly  at  the  middle,  push  down  upon  it. 

When  the  rod  is  bent  is  its  inner  side  stretched  or  compressed? 
Is  its  outer  side  stretched  or  compressed?  (If  in  doubt,  mark 
half-inch  spaces  on  the  two  sides  of  a  long  rubber  eraser,  and 
observe  the  change  in  the  length  of  these  spaces  when  the  rubber  is 
bent  in  the  fingers.)  Account  as  fully  as  you  can  for  the  unequal 
stiffness  of  the  meter  rod  with  respect  to  bending  in  the  two  planes. 

c.  Place  the  three  meter  rods  together  so  as  to  form  a  compound 
rod  of  approximately  square  cross  section.     Test  the  stiffness  of 
this  compound  rod  with 

respect    to    bending   in 

the  two  planes  (Fig.  26). 

In  doing  this  it  will  be 

necessary  to   place  the 

ends  of  the  rod  on  fixed 

supports  and  push  down 

hard     at     the    middle. 

Carefully  observe  whether  bending  in  either  position  is  necessarily 

accompanied  by  slipping  of  one  surface  over  another  where  the 

rods  are  in  contact.     Account  as  fully  as  you  can  for  the  unequal 

stiffness  of  the  set  of  rods  in  the  two  positions. 

If  the  rods  were  nailed  together  along  their  whole  length,  do 
you  think  the  stiffness  would  be  increased  for  the  first  position 
shown  in  the  figure?  Do  you  think  it  would  be  for  the  second 
position?  Give  reasons  for  your  opinion. 

d.  Test  the  relative  stiffness  of  the  metal  rod  and  tube,  and 
account  for  the  results.    (They  contain  equal  quantities  of  the  same 
material.) 

COLEMAN'S  NEW  MANUAL  —  5 


FIG.  26. 


66 


STATICS  OF   SOLIDS 


Experiment  33. —  To  assemble  the  members  of  a  model  bridge 
truss,  and  to  study  their  function  as  parts  of  the  whole. 

Apparatus.  —  A  separable  model  of  the  Pratt  bridge  truss 
(Fig.  27). 

[Short  wire  rods  permanently  inserted  in  the  ends  of  the  struts, 
a,  slip  loosely  through  holes  in  the  top  and  bottom  members,  b  \ 
the  tie-rods,  cy  are  each  provided  with  a  thumbscrew  at  the  top, 


FIG.  27. 

by  which  they  are  tightened.  Suitable  dimensions  for  the  truss  are  : 
length  100  cm.,  height  15  cm.,  cross  section  of  top  and  bottom 
members  and  struts  half  inch  square.  The  tie-rods  are  slender 
rods  of  iron  or  steel ;  the  other  members  of  hard  wood.] 

Experimental  Work.  —  a.  Put  the  truss  together,  and  test  its 
stiffness  when  the  tie-rods  are  tight  and  also  when  they  are  loose. 
Observe  whether  the  tension  of  the  tie-rods  increases  when  the 
truss  is  carrying  a  load.  (This  can  be  tested  by  noting  the  pitch 
of  the  sound  when  the  rods  are  plucked.  The  greater  the  tension 
the  higher  the  pitch.) 

b.  Test  the  stiffness  of  the  truss  when  inverted,  and  account  for 
the  result,  noting  particularly  the  behavior  of  the  tie-rods. 

c.  Observe  and  account  for  the  curvature  of  the  truss  when  the 
rods  are  overtightened. 

d.  The  parts  or  members  of  the  truss  are  the  top  and  bottom 
chords,  the  struts  (the  vertical  members),  the  end  braces,  and  the 
tie-rods.     Which  of  these  are  "  tension  members  "  and  which  are 
"compression   members"?      Which  require  stiffness?      Account 
for  the  stiffness  of  the  truss  as  a  whole. 


V.     DYNAMICS    AND    MACHINES 


EXERCISE  1 6. 


FALLING   BODIES:  WHITING'S 
METHOD 


References.  —  Adams,  28-32;  Colenian,  91-98;  Car.  &  C., 
33-34,  60-6 1  ;  Ches.  G.  and  T.,  114-118;  Head.  Br.,  39,  78- 
79,  81  ;  Hoad.  EL,  42-43,45;  Mumper,  55-56;  Mil.  &  G., 
38-47;  Went.  &  H.,  168-171. 

Experiment  34.  —  To  find  the  acceleration  of  a  falling  body. 

Apparatus.  —  A  long  stick  suspended  to  swing  as  a  pendulum 
(Fig.  28);  meter  rod;  ball;  carbon  paper;  thread;  pins; 
matches ;  watch  or  small  clock  with 
seconds  dial ;  large  piece  of  cloth. 

[For  the  pendulum  use  a  stick  from 
1.5  to  3  m.  long,  of  rectangular  cross 
section  about  2  by  4  cm.  Suspend  it 
by  a  strip  of  canvas  or  leather,  with  its 
wider  side  turned  toward  the  suspended 
ball.  A  strip  of  carbon  paper  is  fastened 
at  top  and  bottom  of  the  pendulum, 
with  paper  beneath  to  receive  the  im- 
pression. The  ball  must  be  heavy 
enough  to  hold  the  pendulum  at  a  con- 
siderable angle,  as  shown  in  the  figure; 


if  of  wood,  it  should  not  be  less  than  /////////////////////////////// 
about  5  cm.  in  diameter.  For  a  long 

pendulum,  an  iron  ball  about  3  cm.  in  diameter  may  be  neces- 
sary. The  apparatus  must  be  so  adjusted  that  the  suspended 
ball  just  touches  the  pendulum  when  the  latter  hangs  vertical.] 

67 


68  DYNAMICS  AND   MACHINES 

Experimental  Work.  —  Fold  the  cloth  into  a  small  mat  and 
place  it  on  the  floor  so  that  the  ball  will  fall  on  it.  Place  a  strip 
of  white  paper  under  the  carbon  paper  at  top  and  bottom  of  the 
pendulum.  This  strip  should  be  as  long  as  the  carbon  paper 
and  a  centimeter  or  more  wider  than  the  pendulum.  Fold  the 
extra  width  over,  make  a  sharp  crease,  open  out  the  fold  at  a 
right  angle,  and  fasten  to  the  side  of  the  pendulum  with  two  pins 
(out  of  the  way  of  ihe  falling  ball).  Adjust  the  ball  and  pendu- 
lum as  shown  in  the  figure,  by  means  of  a  thread  passing  over  the 
three  nails.  The  ball  should  hang  near  the  middle  of  the  paper. 
Without  letting  the  thread  slip  on  the  nails,  strike  the  ball  against 
the  carbon  paper,  marking  its  position  by  the  dot  thus  made  on 
the  paper  beneath.  Stop  the  swinging  of  the  ball  (rotation,  due 
to  the  untwisting  of  the  thread,  does  not  matter,  but  the  results 
will  be  worthless  if  the  ball  is  swinging  at  all),  then  burn  the 
thread  between  the  upper  nails.  The  pendulum  should  strike  the 
ball,  making  a  dot  on  the  lower  paper.  Measure  the  distance 
between  the  upper  and  lower  dots. 

Make  a  second  trial ;  but  before  doing  so,  mark  the  dots  al- 
ready made  on  the  paper,  so  they  will  not  be  mistaken  for 
new  ones.  It  is  better  to  replace  the  paper  by  a  new  piece 
after  a  few  trials.  If  the  second  result  does  not  differ  by  more 
than  i  cm.  from  the  first,  take  the  average  of  the  two.  If  the 
difference  is  greater  than  i  cm.,  make  further  trials  till  you  get 
three  or  more  results  agreeing  within  i  or  2  cm.,  and  take  their 
average.  Call  the  average  distance  s. 

The  ball  falls  s  cm.,  while  the  pendulum  is  swinging  to  a  vertical 
position,  i.e.  while  it  is  making  half  a  swing  in  one  direction.  To 
determine  this  time,  set  the  pendulum  swinging,  and  count  the 
number  of  swings  it  makes  in  exactly  60  sec.,  timing  with  the  second- 
hand of  a  watch.  Repeat,  if  you  are  at  all  doubtful  of  the  result. 

Data  and  Computations.  —  The  rate  of  the  pendulum  does  not 
change  as  the  arc  through  which  it  swings  grows  less ;  hence  from 
the  number  of  swings  in  60  sec.  you  can  determine  the  time  of 


FALLING   BODIES:    PACKARD'S   METHOD  69 

one  swing.  Half  this  time  is  the  time  it  takes  the  ball  to  fall 
s  cm.  Compute  this  time,  and  call  it  t.  Substitute  your  values 
of  s  and  /  in  the  formula  for  falling  bodies,  and  solve  for  g.  Com- 
pute the  percentage  of  error  of  your  result.  Record  as  follows  :  — 

Distance  the  ball  falls  before  striking  the  pendulum  : 

first  trial  =     cm.;  second  trial  =     cm.;  average,  s  =        cm. 

Number  of  swings  the  pendulum  makes  in  60  sec. : 
first  trial  =       ;  second  trial  =       ;  average  = 

Time  of  £  swing,  or  time  of  fall  of  the  ball,  /,  =        sec. 

Value  ofg  from  the  experiment  =  -^j  =        cm. 

True  value  of  g  =980  cm. 

Error  = 

Percentage  of  error  =         % 

EXERCISE   17.     FALLING  BODIES:  PACKARD'S 
METHOD 

References.  —  Adams,  28-32,  48-51,  56-60;  Coleman,  66,  91- 
106  ;  Car.  &  C.,  33-34,  48,  60-6 1  ;  Ches.  G.  &  T.,  114-118,  156  ; 
Hoad.  Br.,  39,  78-82,  in  a  ;  Hoad.  El.,  42-44,  91  ;  Mumper,  55- 
56,  63,  81,  90  ;  Mil.  &  G.,  38-47,  51-52  ;  Went.  &  H.,  168-173. 

Experiment  35.  —  To 

find  the  relation  between 
the  distance  passed  over 
and  the  time  in  uniformly 
accelerated  motion. 

Apparatus.  —  A  broad 
inclined  plane,  with  an 
auxiliary  incline  (Fig. 
29)  ;  steel  ball,  i  in.  or 


more    in    diameter,    ac- 
curately turned  and  polished ;  large  sheet  of  carbon  paper ;  rule. 
[The  plane  should  be  at  ^ast  16  in.  square,  with  a  width  of  at 


70  DYNAMICS   AND   MACHINES 

least  ii  in.  at  the  side  of  the  auxiliary  plane,  and  must  be  smooth 
and  even.  The  auxiliary  plane  should  be  about  5  in.  long,  and 
provided  with  a  groove  running  exactly  parallel  to  the  top  and 
bottom  of  the  principal  plane.  This  groove  is  so  constructed  that 
the  ball  does  not  drop  on  passing  from  it  to  the  principal  plane. 
Roth  planes  are  inclined  at  an  angle  of  about  15°.  A  spring  clip 
to  hold  the  paper  in  position  at  the  top  is  desirable.  This  device 
for  the  study  of  accelerated  motion  is  due  to  Mr.  John  C.  Packard, 
of  the  Brookline,  Mass.,  High  School.  A  very  complete  and  con- 
venient apparatus  for  this  experiment  is  manufactured  by  the 
L.  E.  Knott  Apparatus  Co.,  Boston.] 

Experimental  Work. — Place  a  large  sheet  of  writing  paper  (not 
smaller  than  8  x  10  in.)  on  the  plane  in  the  position  shown  in 
Figure  29.  Place  the  ball  in  the  groove  of  the  auxiliary  plane,  and 
let  it  roll  down  and  over  the  paper.  Observe  its  path  over  the 
paper,  and  find  by  trial  at  what  point  on  the  auxiliary  plane  the 
ball  must  be  released  to  cross  the  bottom  of  the  paper  near 
the  farther  corner.  This  is  the  path  that  the  ball  should  describe 
when  the  record  is  taken. 

Before  taking  a  record,  see  that  the  edges  of  the  sheet  are 
exactly  parallel  with  the  edges  of  the  plane,  and  that  it  just 
touches  the  foot  of  the  auxiliary  plane.  Hold  the  paper  in  this 
position  while  taking  the  record,  if  a  spring  clip  is  not  provided.  * 
Lay  the  carbon  paper  on  the  record  sheet  (with  the  black  side 
down),  and  release  the  ball  at  the  point  previously  determined* 
The  ball  must  be  freed  from  the  control  of  the  auxiliary  plane 
exactly  at  the  point  where  it  starts  across  the  paper  (or  at  some 
other  definitely  marked  point),  and  its  path  at  that  point  must 
be  parallel  to  the  top  edge  of  the  paper.  Be  sure  you  have  the 
right  adjustment.  Repeat  till  at  least  two  satisfactory  traces  of 
the  path  of  the  ball  are  secured.  (Use  the  other  side  of  the 
paper  for  a  second  trace,  or  take  another  sheet.) 

Take  one  or  more  traces  with  the  paper  extending  lengthwise 
from  right  to  left  (instead  of  from  top  to  bottom).  In  this  case 


FALLING    BODIES:    PACKARD'S   METHOD 


b' 


start  the  ball  higher  up  the  auxiliary  plane,  so  that  it  will  cross  the 
bottom  of  the  sheet  near  the  farther  corner,  as  before. 

Principle  of  the  Method. —  If  any  number  of  equidistant  parallel 
lines  be  drawn  on  a  sheet  on  which  the  ball  has  traced  its  path, 
taking  for  the  first  of  these  lines  the  edge  of  the  paper  at  which 
the  trace  begins,  these  lines  will  divide  the  curve  into  parts  ab\ 
b'J ,  c'd1,  d*e'  (Fig.  30),  which  were  traversed  by  the  ball  in  equal 
times.  This  is  explained  as 
follows  :  The  motion  along  the 
curve  may  be  resolved  into  two 
components  at  right  angles  to 
each  other  —  one  across  the 
plane  (from  left  to  right  in  the 
figure)  and  the  other  down 
the  plane.  These  we  shall  call 
the  horizontal  and  the  downward 
components,  respectively.  The 
horizontal  component  was  wholly 
imparted  on  the  auxiliary  plane. 
It  remains  constant  on  the  prin- 
cipal plane,  since  there  is  no 


B 


FIG.  30. 


force  acting  to  change  it  (friction,  being  inappreciably  small,  is 
disregarded).  If  the  principal  plane  were  horizontal,  the  ball  would 
cover  the  equal  distances  ab,  be,  cdy  and  de  in  equal  times,  the 
velocity  being  constant.  With  the  principal  plane  inclined,  the 
direction  of  the  unbalanced  force  acting  on  the  ball  is  down 
the  plane,  and  it  affects  only  the  downward  component  of  the 
motion.  Knowing,  therefore,  that  the  ball  covers  equal  distances 
from  right  to  left  in  equal  times,  whether  the  plane  is  inclined  or 
not,  it  follows,  as  stated  above,  that  the  equidistant  parallel  lines 
divide  the  curved  path  into  parts  which  the  ball  traversed  in  equal 
intervals  of  time.  During  the  first  of  these  equal  time  intervals 
the  downward  distance  covered  is  bb1 ,  during  the  first  two  intervals 
it  is  cc\  during  the  first  three  drf,  etc.  This  downward  motion 


DYNAMICS   AND   MACHINES 


is  in  no  wise  affected  by  the  horizontal  motion  —  the  ball  would 
make  equal  progress  down  the  plane  if  it  had  a  greater  horizontal 
component  of  motion  or  if  it  had  no  horizontal  motion  at  all.  In 
this  experiment  the  horizontal  component  of  motion  merely  serves 
the  purpose  of  marking  equal  time  intervals. 

Construction  and  Comparison.  —  On  one  of  your  record  sheets 
draw  very  accurately  five  equidistant  parallel  lines,  as  in  Figure  30, 
taking  the  equal  distances  such  that  the  fifth  line  cuts  the  curve 
near  its  lower  end.  The  first  line  AB  must  be  taken  through  the 
point  where  the  ball  passes  from  the  control  of  the  auxiliary  plane 
and  is  free  to  follow  a  curved  path.  Letter  the  sheet  to  correspond 
with  Figure  30.  The  five  lines  mark  off  four  equal  time  intervals. 
Draw  the  horizontal  line  abcde.  Measure  accurately  the  downward 
distances  bb',  cc\  dd* ,  and  ee' .  The  distance  ee'  being  the  greatest, 
it  is  probably  determined  with  the  greatest  accuracy.  It  is  there- 
fore taken  as  the  basis  of  comparison.  Find  the  difference  between 
bb*  and  y1^  ee' ,  between  cc'  and  -^  ee' ,  and  between  dd'  and  T9g-  ee1. 
If  the  work  is  carefully  done,  these  differences  will  not  exceed  i  or 
2  mm.  Record  as  follows  :  — 


TIME  TAKEN 

FOR  THE 
RESPECTIVE 
DISTANCES 

SQUARE  OF 

THE  TIME 

DOWNWARD  DISTANCES 

DIFFERENCE 

Measured 

Computed  from  ee' 

I  interval 

1*=      I 

bb1  =  cm. 

l|l6  ee1  =  cm. 

cm. 

2  intervals 

2*=     4 

cJ  =  cm. 

4|i6  ee'  —  cm. 

cm. 

3  intervals 

32=   9 

dcF  =  cm. 

9|  1  6  eer  =  cm. 

cm. 

4  intervals 

42=16 

ee1  —  cm. 

i6|i6  ee'  =  cm. 

cm. 

Make  a  similar  construction  and  tabulation  of  results  for  the 
other  curves  taken,  varying  the  work,  however,  by  marking  the 
curve  off  into  three  or  five  equal  time  intervals,  instead  of  four,  as 
above.  When  three  intervals  are  taken,  compare  the  first  down- 
ward distance  with  ^  of  the  third,  and  the  second  with  -|  of  the 


THE   SIMPLE   PENDULUM 


73 


third ;  where  five  intervals  are  taken,  compare  the  first  downward 
distance  with  -£%  of  the  fifth,  the  second  with  -fa  of  it,  the  third 
with  2^5  of  it,  and  the  fourth  with  if  of  it. 

Preserve  and  hand  in  the  sheets  on  which  the  curves  were 
taken  and  the  constructions  made,  as  a  part  of  the  record  of  the 
experiment. 

Discussion  (oral  except  the  first  question).  —  i.  What  relation 
does  this  experiment  establish  (within  a  small  limit  of  error) 
between  the  downward  distance  and  the  time  ?  Derive  this 
relation  from  the  tabulated  record. 

2.  How  is  it  known  that  the   horizontal   component   of  the 
motion  of  the  ball  is  constant  ? 

3.  What  is  the  unbalanced  force  acting 
on  the  ball  when  it  is  on  the  principal  plane? 
What  is  its  direction  ?     Is  it  a  constant  or 
a  variable  force  ?     Prove  your  answer. 

4.  What  is  the  direction  of  the  accelera- 
tion of  the  ball?     Why?     Is  it  a  constant 
or  a  variable   acceleration?     How   is   this 
shown  by  the  results?     What  is  the  reason 
for  its  being  so  ? 

EXERCISE    1 8.     THE   SIMPLE 
PENDULUM 

References. — Adams,     76-78,     81-82; 
Coleman,    130-135;    Car.    &    C.,    68-71;, 
Ches.  G.  &T.,  164-166  ;  Hoad.  Br.,  83-85  ; 
Hoad.  EL,  92-95  ;  Mumper,  95  ;  Mil.  &  G., 
224  ;  Went.  &  H.,  189-191. 

Apparatus.  —  A    pendulum    stand    with  FlG-  Si- 

three  pendulums  of  adjustable  length,  one  with  wooden  and  two 
with  iron  or  lead  bobs  (Fig.  31)  ;  watch  or  clock  with  second- 
hand ;  meter  rod. 


74  DYNAMICS  AND    MACHINES 

[A  convenient  and  efficient  adjustable  suspension  is  shown  in 
Figure  31.  A  slanting  notch  is  cut  at  an  angle  of  about  35°  to 

receive  the  thread,  and 

| ("gs]  iu»    a  cork  glued  above,  in 

— ^    which  is  cut  a  slit  to 

FIG'  32'  receive  the  thread.  The 

friction  in  the  cork  holds  the  pendulum.  The  pendulum  clamp 
shown  in  Figure  32  is  also  especially  adapted  to  the  requirements 
of  the  exercise.  It  can  be  clamped  to  any  support  rod.] 

Experiment  36.  To  find  whether  the  amplitude  of  a  pendulum 
affects  its  rate. 

Experimental  Work. — -a.  Adjust  the  two  pendulums  with  iron 
bobs  to  exactly  the  same  length,  making  them  about  as  long  as 
the  apparatus  will  permit.  Test  the  equality  of  their  lengths  by 
careful  measurement,  and  also  by  starting  them  together  with  equal 
amplitudes.  If  there  is  even  a  very  slight  difference  in  their 
lengths,  the  shorter  will  slowly  gain  on  the  other,  and  the  differ- 
ence will  begin  to  be  noticeable  in  a  minute  or  so. 

After  securing  exact  adjustment,  start  the  pendulums  together, 
giving  one  an  amplitude  of  not  more  than  5°  and  the  other  an 
amplitude  of  30°  to  35°.  Observe  whether  the  pendulums  con- 
tinue for  at  least  a  minute  to  begin  and  end  their  swings  together. 
A  difference  as  small  as  a  tenth  of  a  swing  can  be  seen,  whereas  a 
difference  of  one  whole  swing  is  the  least  that  would  be  detected 
by  counting  the  number  of  swings  made  by  each  pendulum  in  a 
given  tirtie.  Do  not  count,  but  observe.  Verify  the  result  by  a 
second  trial,  giving  the  larger  amplitude  to  the  other  pendulum. 
About  what  difference,  if  any,  do  you  observe  in  the  rates  of  the 
two  pendulums? 

b.  Again  start  the  pendulums  together,  giving  one  an  amplitude 
of  about  6°  and  the  other  less  than  3°.     Let  them  swing  thus  for 
a  minute  or  more.     How  do  their  rates  compare  ? 

c.  What  do  the  above  tests  show  concerning  the  effect  of  the 
amplitude  of  a  pendulum  on  its  rate? 


THE   SIMPLE   PENDULUM 


75 


Experiment  37. —  To  find  whether  the  rate  of  a  pendulum  is 
affected  by  either  its  mass  or  its  material. 

Experimental  Work. — Adjust  the  pendulum  with  a  wooden 
bob  to  the  same  length  as  one  with  an  iron  bob.  The  pendulums 
should  be  long.  The  length  is  measured  from  the  point  of  sup- 
port to  the  middle  of  the  bob.  Start  the  two  pendulums  together, 
with  equal  amplitudes  (not  above  10°),  and  observe  whether  one 
gains  on  the  other  in  a  minute  or  more.  How  do  you  find  the 
rates  of  the  pendulums  to  be  affected  by  the  fact  that  they  are  of 
unequal  mass  and  of  different  materials  ? 

Experiment  38.  —  To  find  the  relation  between  the  period  of  a 
pendulum  and  its  length. 

Experimental  Work.  —  Adjust  the  three  pendulums  to  lengths 
having  the  ratio  of  i,  \,  and  ^-.  Lengths  of  36  in.,  9  in.,  and  4  in. 
will  be  most  convenient,  if  the  height  of  the  support  will  permit. 
Count  the  number  of  single  vibrations  that  each  of  the  pendulums 
makes  in  exactly  60  sec. 

If  you  have  time,  test  the  ratio  of  the  periods  of  the  pendulums 
by  starting  together  the  36-in.  and  the  9-in.  pendulums,  and  observe 
how  many  swings  of  the  shorter  occur  during  one  swing  of  the 
longer.  Test  the  36-in.  and  the  4-in.  pendulums  in  the  same  way. 

Data  and  Computations.  —  Let  /  denote  the  length  of  a  pendu- 
lum and  /  the  time  of  one  vibration.  Compute  for  each  of  the 
pendulums  the  value  of  the  ratio  V/:/  (to  be  expressed  deci- 
mally) .  Record  in  tabular  form,  as  follows  :  — 


LENGTH  =  / 

WHOLE  TIME 

No.  OF  SWINGS 

TIME  OF  i 
VIBRATION  =/ 

V/ 

V/:/ 

36  in. 

60  sec. 









9  in. 

60  sec. 





— 



4  in. 

60  sec. 





— 



76  DYNAMICS   AND   MACHINES 

Discussion. —  i.  If  there  were  no  errors,  the  value  of  the  ratio 
V7:  /  would  be  the  same  for  the  three  pendulums.  Compute  the 
percentage  of  difference  between  the  greatest  and  the  least  of 
these  values.  This  should  not  exceed  2  %. 

2.  What  is  the  probable  source  of  the  greatest  error  in  the 
experiment  ? 

3.  From  the  equal  values  of  the  ratio  V/:/for  all  pendulums, 
derive  the  proportion  between  the  lengths  of  any  two  pendulums, 
4  and  /2,  and  their  periods,  /A  and  /2« 

EXERCISE    19.     THE   WHEEL  AND   AXLE 

References.  —  Adams,  100-103,  112-113  ;.  Coleman,  159-161, 
168-169;  Car.  &  C.,  89-92,  96-97;  Ches.  G.  &  T.,  143-144, 
147;  Hoad.  Br.,  93-94,  104-105;  Hoad.  El.,  101-105,  113- 
114;  Mumper,  83-85,  89  ;  Mil.  &  G.,  207,  212-213  ;  Went.  &  H., 
206-211. 

Definitions.  —  In  this  and  the  following  exercises  on  machines, 
the  same  kind  of  quantity  is  always  represented  by  the  same 
letter.  The  definitions  of  these  quantities  and  the  letters  by 
which  they  are  represented  are  as  follows  :  — 

The  body  moved  by  a  machine  is  called  the  load.  The  resist- 
ing force  that  the  load  exerts  while  being  moved  is  called  the 
resistance,  and  it  is  denoted  by  R.  In  these  laboratory  exercises 
the  machine  is  used  to  raise  the  load ;  in  which  case  the  work  is 
done  against  gravity,  and  the  resistance  R  is  the  weight  of  the  load. 

The  body  that  does  the  work,  or  supplies  the  energy  for  raising 
the  load,  is  called  the  agent.  The  force  that  the  agent  must  exert 
to  maintain  equilibrium,  or  the  force  that  would  be  required  to 
do  the  work  if  there  were  no  friction,  is  called  the  static  effort, 
and  is  denoted  by  E8.  The  force  that  the  agent  must  exert  to 
move  the  load  is  necessarily  greater  than  Es.  It  is  called  the 
working  effort,  and  is  denoted  by  Ew.  In  these  laboratory  exer- 
cises the  agent  consists  of  one  or  more  standard  masses  (weights) , 


THE   WHEEL  AND   AXLE  JJ 

and  their  united  weight  constitutes  the  static  effort  E8  or  the 
working  effort  EW9  according  to  whether  it  maintains  equilibrium 
or  raises  the  load. 

The  distance  through  which  the  effort  (or  the  agent)  acts  is 
called  the  effort  distance,  and  is  denoted  by  De ;  and  the  vertical 
distance  through  which  the  resistance  is  overcome  (or  the  load  is 
raised)  is  called  the  resistance  distance,  and  is  denoted  by  J9r. 

According  to  the  rule  for  the  measure  of  work  (see  text),  the 
work  done  by  the  working  effort  (or  the  agent)  is  denoted  by 
EwDe,  and  the  work  done  against  the  resistance  (or  upon  the 
load)  is  denoted  by  RDr.  In  other  words,  EwDe  denotes  the 
energy  transferred  from  the  agent  to  the  machine,  and  RDr 
denotes  the  energy  transferred  from  the  machine  to  the  load. 

The  efficiency  of  a  machine  is  defined  as  the  ratio  of  the  work 
done  on  the  load  (the  useful  work)  to  the  total  energy  expended 
by  the  agent ;  i.e. 

Efficiency  =  -^21. 
EwDt 

Experiment  39. —  To  find  the  mechanical  advantage  and  the 
efficiency  of  a  wheel  and  axle. 

Apparatus.  —  Mounted  axle  carrying  two  wheels  of  different 
diameters,  with  cords  attached  and  a  hook  at  the  end  of  each 
cord ;  meter  rod ;  set  of  weights  running  to  500  g.  or,  better,  to 
1000  g. 

[The  " universal  laboratory  weights"  shown  in  Figure  21  are 
recommended  as  most  convenient  for  all  experiments  with 
machines.  An  ordinary  set  of  weights  can  be  used  by  tying  a 
loop  of  stout  thread  to  each,  by  which  they  can  be  hung  on  hooks 
attached  to  the  ends  of  the  cords.  It  is  more  convenient,  how- 
ever, to  tie  a  small  bucket  or  pan  to  the  cord  to  hold  the  weights. 
If  the  set  runs  to  1000  g.,  weights  smaller  than  10  g.  are  un- 
necessary ;  if  the  largest  is  500  g.,  5  g.  is  the  smallest  required. 
Weights  are  more  accurate  and  are  better  in  other  respects  for 
determining  the  effort  than  the  draw  scale.] 


DYNAMICS   AND    MACHINES 


Experimental  Work.  —  a.  Hang  one  or  more  of  the  largest 
weights  (the  load)  on  the  cord  attached  to  the  axle ;  and  hang 
just  sufficient  weights  (the  agent)  on  the  cord  attached  to  one  of 
the  wheels  to  raise  the  load  slowly  (Fig.  33).  If  a  bucket  or  pan 
for  holding  these  weights  is  attached  to  the  cord,  its  weight  must 
be  included  as  part  of  the  effort.  It  will  probably  be  found  that, 
on  account  of  varying  friction,  the  motion  is  not  uniform  ;  but, 
on  the  average,  the  motion  should  neither  be  accelerated  nor 
retarded.  Record  the  weight  of  the  load  R,  and  the  effort  with 
the  load  rising.  The  latter  is  the  working  effort  Ew. 

Find  the  effort  required  to  maintain  steady 
motion  as  the  load  slowly  descends.  (Reduce 
the  effort  by  removing  weights,  but  leave  the 
load  unchanged.)  The  average  of  these  two 
values  of  the  effort  is  the  static  effort  Es, 
(Why?) 

Measure  the  distance  De  through  which  the 
effort  acts  (the  distance  that  the  agent  descends) 
and  the  distance  DT  through  which  the  load  is 
raised,  when  the  load  is  raised  from  the  lowest 
to  the  highest  point  that  the  adjustment  of  the 
apparatus  will  permit.  (It  will  be  found  most 
convenient  and  most  accurate  to  measure  all 
distances  from  the  level  of  the  table  or  the  level  of  the  floor, 
according  to  the  portion  of  the  apparatus.  For  example,  the 
height  of  the  load  above  the  floor  at  the  start  subtracted  from 
its  height  above  the  floor  after  it  has  been  raised,  gives  the 
distance  Dr.) 

Measure  the  diameters  of  the  wheel  and  the  axle.  (If  it  is 
inconvenient  to  measure  these  diameters  directly,  measure  the 
length  of  the  cord  that  goes  just  once  around  the  circumference, 
and  divide  this  length  by  3.1416.) 

b.  If  time  permits,  repeat  the  experiment,  using  the  axle  and 
the  other  wheel  or  the  two  wheels,  regarding  the  smaller  one  as  the 
axle  in  the  latter  case. 


THE   WHEEL   AND    AXLE 
Data  and  Computations.  —  Record  as  follows  :  — 


79 


a 

b 

Weight  of  the  load  R          .         .         .         . 

g. 

g- 

Fff     t      *th  1      \    '  '                     V          ff     t  F 

-  -  ff 

Effort  with  load  descending 

g- 
g- 

&• 

g- 

Distance  through  which  effort  acts,  De 

cm  % 

Distance  through  which  load  is  raised,  Dr 

cm. 

cm. 

Radius  of  wheel  Ae  (arm  of  the  effort) 

cm. 

cm. 

Radius  of  axle  Ar  (arm  of  resistance) 

cm. 

cm. 

COMPUTATIONS 


Average  or  static  effort  Es  ... 

Mechanical  advantage  (by  definition)  =  7?  -=-  Es 

Mechanical  advantage  (from  the  dimensions  of 
the  machine)  =  Ae  -f-  Ar 

Work  done  on  the  load  =  RDr  . 
Work  done  by  the  agent  =  EwDe 
Efficiency  of  the  machine  =  RDr  -f-  EluDe  . 


-  g.-cm. 

-  g.-cm. 


-  g.-cm. 

-  g.-cm. 


Discussion.  —  i.  Show  from  the  principle  of  moments  of  force 
that  the  ratios  R  :  E8  and  Ae :  Ar  should  be  equal.  (The  effort 
and  the  resistance  tend  to  turn  the  wheel  and  axle  in  opposite 
directions.)  Which  of  these  ratios  determines  what  the  value  of 
the  other  must  be  for  a  given  wheel  and  axle? 

2.  It    can    be    proved    geometrically    that   De :  Dr :  :  Ae :  Ar. 
(Prove  it.)     Compare  your  experimental  values  for  these  ratios. 

3.  From  the  proportions  given  in  the  first  two  questions,  show 
that  R\Es\\De\Dr  or  E8De  =RDr.     It  follows  that, 

~ffi     ' 

Efficiency  = 


8O  DYNAMICS  AND   MACHINES 

that  is,  the  efficiency  is  equal  to  the  ratio  of  the  static  effort  to 
the  working  effort.  Compute  the  efficiency  from  this  ratio,  and 
compare  the  result  with  the  value  obtained  from  RDr  -r-  EwDe. 

4.  Prove  that  the  mechanical  advantage  of  the  wheel  and  axle 
is  equal  to  the  ratio  De :  Dr.  State  this  relation  in  words. 

EXERCISE    20.     PULLEYS 
i 

References.  —  Adams,  115-116 ;  Coleman,  162-165,  168-169; 
Car.  &  C.,  98-100;  Ches.  G.  &  T.,  148-155;  Hoad.  Br.,  107- 
no;  Hoad.  EL,  116-119;  Mumper,  88;  Mil.  &  G.,  204-207; 
Went.  &  H.,  212. 

Apparatus.  —  A  single  and  two  double  or  triple  pulleys  ;  frame 
with  screw  hooks  to  support  the  pulleys  (Fig.  34);  meter  rod; 
stout,  flexible  cord  (heavy  fishing-line)  ;  set  of  weights  to  1000  g. ; 
small  hook  or  a  weight  bucket,  if  the  weights  are  not  provided  with 
hooks. 

Experiment  40.  —  To  find  the  mechanical  advantage  and  the 
efficiency  of  a  single  fixed  pulley. 

Experimental  Work.  —  Suspend  a  pulley  (a  single  one,  if  pro- 
vided), and  pass  a  cord  over  it.  Fasten  the  largest  weight  (the 
load)  to  one  end  of  the  cord.  Tie  a  loop  in  the  cord  on  the  other 
side  of  the  pulley,  at  a  convenient  height  (attach  the  weight 
bucket  or  a  hook  to  the  loop,  if  the  weights  have  no  hooks),  and 
hang  just  sufficient  weights  in  it  to  raise  the  load  slowly  and 
steadily.  (If  the  remaining  weights  of  the  set  are  not  sufficient 
for  this,  use  a  smaller  weight  for  the  load.)  Record  the  weight 
of  the  load  R,  and  the  working  effort  Ew  (the  effort  with  the  load 
rising). 

Find  the  effort  required  to  maintain  steady  motion  as  the  load 
slowly  descends.  (Reduce  the  effort  by  removing  weights,  but 
leave  the  load  unchanged.)  The  average  of  these  two  values  of 
the  effort  is  the  static  effort  Et.  (Why  ?) 


PULLEYS 


81 


FIG.  34. 

Data  and  Computations. — As  in  the  case  of  the  wheel  and  axle, 
it  can  be  shown  that  the  efficiency  of  the  fixed  pulley  is  equal  to 
the  ratio  of  the  static  effort  E8  to  the  working  effort  Ew.  Take 
this  ratio  as  the  measure  of  the  efficiency.  Record  as  follows  :  — 

Weight  of  the  load  R  =       g. 

Effort  with  load  rising,  or  working  effort,  Ew  =       g. 

Effort  with  load  descending  =       g. 

Average  or  static  effort,  Es  =       g. 
Experimental  value  of  mechanical  advantage  =  R  -r-  Es    = 

True   value   of   mechanical   advantage    (=  number  of 

parts  of  the  cord  supporting  the  load)  .    =  i 

Percentage  of  error  =         % 

Efficiency  of  the  fixed  pulley  =  Es  -+-  Ew  =         % 
COLEMAN'S  NEW  MANUAL  —  6 


82 


DYNAMICS  AND    MACHINES 


Experiment  41. —  To  find  the  mechanical  advantage  and  tht 
efficiency  of  a  single  movable  pulley  and  of  a  combination  of  fixed 
and  movable  pulleys. 

Experimental  Work. — a.  When  a  movable  pulley  is  used,  it 
becomes  a  part  of  the  load  to  be  raised.  Weigh  every  movable 
pulley  used  (unless  its  weight  is  recorded  on  it),  and  add  its  weight 
as  a  part  of  the  resistance  R. 

Adjust  a  fixed  and  a  movable  pulley  as  shown  in  Figure  34.  Use 
the  looo-g.  weight  (or  the  largest  provided)  as  the  load.  Find 
the  working  effort  and  the  effort  with  the  load  slowly  descending, 
as  in  the  preceding  experiment. 

Measure  the  distance  De  through  which  the  effort  acts  (the  dis- 
tance that  the  agent  descends)  and  the  distance  Dr  through  which 
the. load  is  raised  when  the  load  is  raised  from  the  lowest  to  the 
highest  convenient  point  (which  should  be  at  least  25  cm.).  (It 
will  be  most  convenient  and  most  accurate  to  measure  all  dis- 
tances from  the  bottom  of  the  support,  or  from  the  table  top,  if 
that  is  directly  under  the  pulleys.) 

b.  Repeat  the  experiment,  using  two  or  three  fixed  and  two  or 
more  movable  pulleys.  Use  two  or  more  of  the  heaviest  weights 
for  the  load,  and  remember  to  include  the  weight  of  the  movable 
pulleys  as  a  part  of  the  resistance  R.  Make  a  drawing  of  the 
arrangement  of  pulleys  used. 

Data  and  Computations.  —  Record  measurements  and  computa- 
tions as  follows :  — 


a 

b 

Weight  of  the  load  (including  weight  of  mova- 

ble pulleys)  R           

g- 

'  g- 

Effort  with  load  rising  (working  effort),  Ew  . 

g- 

g- 

Effort  with  load  descending   .... 

g- 

g- 

Distance  thrgugh  which  effort  acts,  De   . 

cm. 

cm. 

Distance  through  which  load  is  raised,  Dr 

cm. 

cm. 

THE  INCLINED    PLANE 


COMPUTATIONS 


a 

b 

Average  or  static  effort,  Es 
Experimental  value  of  mechanical  advantage 

True  value  of  mechanical  advantage  (number 
of  parts  of  cord  supporting  load) 

Percentage  of  error  of  mechanical  advantage  . 

2 

—  g. 

o/ 
/o 

g.-cm. 
—  g.-cm. 

Work  done  by  the  agent  =  EwDe  . 
Efficiency,  computed  from  RDr-±EwDe 
Efficiency,  computed  from  Es  -=-  Ew      -   . 

g.  cm. 
g.-cm. 

/o 

o/ 
—  /o. 

Discussion  (Oral).  —  i.  By  definition,  the  efficiency  of  a  machine 
is  RDr  -r-  EwDe.  Prove  that  this  is  equal  to  Es  -r-  Ew  (a)  for  a 
single  fixed  pulley,  (U)  for  a  single  movable  pulley,  (c)  for  any 
combination  of  fixed  and  movable  pulleys. 

2.  Prove  that  the  mechanical  advantage  of  any  combination  of 
pulleys  is  equal  to  the  ratio  De :  Dr. 


EXERCISE    21.     THE   INCLINED   PLANE 

References.  —  Adams,  58,  118;  Coleman,  166-169;  Car.  & 
C.,  101-102  ;  Ches.  G.  &  T.,  156;  Hoad.  Br.,  in  ;  Hoad.  EL, 
120;  Mumper,  90;  Mil.  &  G.,  214;  Went.  &  H.,  46. 

Experiment  42.  —  To  find  the  mechanical  advantage  and  the 
efficiency  of  an  inclined  plane. 

Apparatus.  —  An  inclined  plane,  with  single  fixed  pulley  at  top 
(Fig.  35);  roller  or  car,  with  its  weight  marked  on  it:  metric 
rule  •  set  of  weights. 


84 


DYNAMICS   AND   MACHINES 


Experimental  Work.  —  a.  Set  the  plane  at  an  angle  of  about 
25°.  (The  angle  need  not  be  measured.)  Place  the  roller  or 
car  on  the  plane,  pass  a  cord  from  it  over  the  pulley,  and  attach 
just  sufficient  weights  to  the  cord  to  draw  the  roller  (or  car)  slowly 
and  steadily  up  the  plane  (Fig.  35).  (If  a  car  and  weights  to 

1000  g.  are  provided, 
more  accurate  results 
will  be  obtained  by  load- 
ing the  car  with  one  or 
more  of  the  heavier 
weights.)  Record  the 
weight  of  the  load./?,  and 
the  working  effort  Ew. 

Find  the  effort  re- 
quired to  maintain 
steady  motion  as  the 
load  rolls  slowly  down 
the  plane. 

Measure  the  length  Z  of  the  plane  along  its  under  edge,  from 
its  lower  end  to  the  straight,  vertical  edge  of  the  support.  Meas- 
ure the  height  H  of  the  plane  at  the  vertical  edge  of  the  support, 
from  the  under  edge  of  the  plane  to  the  upper  edge  of  the  base. 

b.  Repeat  the  experiment  with  the  plane  at  an  angle  of  about 
45°. 

Data  and  Computations.  —  Record  as  follows  :  — 


FIG.  35. 


a 

b 

Weight  of  the  load  R          .          .         .         . 

g. 

g- 

Effort  with  the  load  rising  (working  effort),  Ew 

g. 

g- 

Effort  with  load  descending 

g- 

g- 

Length  of  the  plane  L         ..          .         .         . 

cm. 

cm. 

Height  of  the  plane  H 

GEARED   WHEELS 


COMPUTATIONS 


a 

b 

Average  or  static  effort  Es            ... 
Mechanical  advantage,  from  R  -f-  Es  . 
Mechanical  advantage,  from  L  -r-  //   . 
Percentage  of  difference     .... 

Work  done  on  the  load  in  rolling  it  up  the 
plane  -  RH   

Work  done  by  the  agent  —  EWL 
Efficiency,  computed  from  RH  "-*-  EWL 
Efficiency,  computed  from  Es  -f-  Ew 

g- 
g.-cm. 

g.-cm. 
g.-cm. 

g.-cm. 

/o 

Discussion  (Oral) .  —  Taking  RH-^  EWL  as  the  definition  of  the 
efficiency  of  the  inclined  plane,  prove  it  to  be  equal  to  £3  -~-  Ew. 

EXERCISE    22.     GEARED   WHEELS 
(  INVENTIVE) 

Experiment  43.  —  To  find  the  mechanical  advantage  and  the 
efficiency  of  a  train  of  geared  wheels. 

Apparatus.  —  Set  of  geared  wheels  (Fig.  36),  mounted  on  a 
suitable  support,  with  a 
cord  to  support  the  load 
and   a   stout   thread   to 
the 


support 
weights     to 
meter  rod. 


agent; 
TOGO    g. ; 


Suggestion.  —  The 
pupil  is  left  to  work  out 
the  details  of  this  ex- 
periment and  the  form 
of  record  for  himself.  The  mechanical  advantage  can  be  found 
experimentally  by  three  independent  methods,  and  the  efficiency 
by  two.  Employ  any  or  all  of  these  that  occur  to  you. 


FlG* 


VI.    MOLECULAR   PHENOMENA 

EXERCISE    23.     COHESION   AND   ADHESION 

References.  —  Adams,  126-132;  Coleman,  188-193;  Car.  & 
C.,  17-18;  Ches.  G.  &  T.,  62;  Hoad.  Br.,  28;  Hoad.  EL,  31, 
130;  Mumper,  22  ;  Mil.  &  G.,  157-159  ;  Went.  &  H.,  142,  144, 
146. 

Experiment  44.  —  To  study  the  effect  of  distance  on  molecular 
attraction,  and  to  study  the  behavior  of  liqtiids  in  contact  with 
solids. 

Apparatus.  —  Two  pieces  of  plate  glass  and  two  of  window 
glass,  each  about  6  cm.  square ;  piece  of  glass  coated  with  paraf- 
fme ;  bottle  containing  a  little  mercury ;  sealed  bottle  containing 
clean  mercury  and  very  small  pieces  of  glass ;  vessel  of  water ; 
dropping  tube  ;  mop  cloth. 

[The  pieces  of  glass  should  be  between  2  mm.  and  4  mm.  in 
diameter,  and  there  should  be  just  enough  mercury  in  the  bottle 
to  cover  about  one  third  of  the  bottom.  The  surface  of  the  mer- 
cury must  be  clean  and  bright.  Sealing  the  bottle  with  wax  will 
preserve  the  mercury  from  other  use,  and  keep  it  clean.] 

Experimental  Work.  —  a.  Have  the  pieces  of  plate  glass  clean 
and  dry.  Press  them  firmly  together,  then  note  the  force  re- 
quired to  pull  them  apart.  Is  cohesion  between  them  great 
enough  to  lift  one  of  them  by  means  of  the  other  ? 

b.  Try  the  two  pieces  of  window  glass  in  the  same  way.  How 
do  the  results  compare  with  the  preceding?  The  surfaces  of  the 
plate  glass  are  quite  accurately  plane,  while  those  of  the  window 
glass  are  more  or  less  uneven  and  wavy.  The  difference  in  the 
results  in  the  two  cases  is  due  to  this  difference  in  the  surfaces. 

86 


COHESION   AND   ADHESION  87 

Hence  the  experiments  illustrate  a   necessary  condition  for   the 
existence  of  cohesion.     What  is  this  condition  ? 

c.  Again  take  the  pieces  of  plate  glass,  dip  them  in  water  to 
moisten  their  surfaces,  and  press  them  together  as  before.     Note 
the^  force  now  required  to  pull  them  apart.     How  does  it  compare 
with  the  force  required  when  the  plates  are  dry  ?     The  thin  layer 
of  water  adheres  to  the   glass   surface  on  each  side,  forming  a 
connecting  link. 

Is  adhesion  between  water  and  glass  stronger  or  weaker  than 
cohesion  within  a  piece  of  glass?  How  is  this  shown?  Why  is 
adhesion  between  water  and  glass  stronger  than  cohesion  between 
the  two  pieces  of  plate  glass?  Is  cohesion  in  water  stronger  or 
weaker  than  adhesion  between  water  and  glass?  How  is  this 
shown  ? 

d.  CAUTION.    In  handling  mercury,  be  careful  not  to  get  any  of 
it  on  jewelry.     It  unites  with  gold  and  silver,  forming  an  amalgam 
which  discolors  the  surface. 

By  means  of  the  dropping  tube  transfer  a  small  drop  of  mercury 
from  the  bottle  to  a  piece  of  glass.  Flatten  the  drop  with  the 
finger,  then  observe  the  effect  of  removing  the  finger.  The  be- 
havior of  the  drop  does  not  prove  that  there  is  no  adhesion 
between  mercury  and  glass.  What  does  it  prove?  Why  does 
the  drop  of  mercury  not  flatten  out  and  spread  over  the  glass  as  a 
drop  of  water  would  ? 

With  the  finger  or  the  point  of  your  pencil,  detach  a  very  small 
bit  from  the  drop.  Is  this  smaller  portion  more  or  less  nearly 
spherical  than  the  larger  portion?  Why?  Pour  the  drop  of 
mercury  into  your  hand  and  return  it  to  the  bottle. 

e.  Take  the  sealed  bottle  containing  mercury  and  bits  of  glass. 
Incline  it  slightly  from  side  to  'side  so  that  the  mercury  will  run 
about  over  the  bottom  of  the  bottle,  and  note  the  behavior  of  the 
bits  of  glass   toward  the  mercury.     What  evidence  of  adhesion 
between  glass  and  mercury  do  you  observe? 

/.  Observe  the  behavior  of  a  drop  of  water  on  the  paraffined 
surface  of  the  piece  of  glass.  Do  you  find  cohesion  within  water 


88 


MOLECULAR   PHENOMENA 


stronger  or  weaker  than  adhesion  between  water  and  paraffine? 
Do  you  infer  that  adhesion  between  water  and  paraffine  is  greater 
or  less  than  between  water  and  glass? 

EXERCISE  24.     SURFACE  TENSION  AND  CAPILLARITY 

References.  —  Adams,  150-156  ;  Coleman,  195-200  ;  Car.  &  C., 
113-122;  Ches.  G.  &  T.,  63-65;  Hoad.  Br.,  119-126;  Hoad. 
EL,  130-136;  Mumper,  23-25;  Mil.  &  G.,  160-167;  Went.  & 
H.,  145,  147. 

Experiment  45. —  To  study  various  phenomena  due  to  surface 
tension. 

Apparatus.  —  Tumbler  of  clean  water;  pins;  two  small  slivers 
of  wood  (toothpicks)  ;  very  slender  rubber  band ;  lifter  made  of 
wire,  for  placing  pins  on  water  (Fig.  37) ; 
small  bottle  of  alcohol ;  glass  rod  ;  dish  of  soap 
solution ;  wire  ring  about  3  in.  in  diameter, 
with  extension  of  wire  for  handle,  and  with 
thread  tied  loosely  across  the  ring  (Fig.  38)  ; 
bottle  containing  a  drop  of  oil  suspended  in  a 
solution  of  alcohol  and  water  of  its  own  density. 
[For  a  good  soap  solution,  put  2  oz.  of 
Castile  soap,  shaved  thin,  in  i  pt.  of  dis- 
tilled or  rain  water.  Shake,  pour  off  the 
clear  solution,  and  add  to  it  \  pt.  glyc- 
erine, and  stir.  To  prepare  the  sus- 
pended drop  of  oil,  pour  a  very  little 
water  into  the  bottle  and  add  an  equal 
or  greater  quantity  of  alcohol  without 
shaking.  This  will  leave  the  mixture 
somewhat  denser  at  the  bottom.  Insert 
2  or  3  large  drops  of  olive  or  machine 
oil  by  means  of  a  dropping  tube.  Slowly 
pour  in  more  alcohol,  if  necessary,  till 
the  drop  sinks  below  the  surface.]  FIG.  38. 


FIG.  37. 


SURFACE  TENSION   AND   CAPILLARITY  89 

Experimental  Work.  —  a.  Place  a  pin  on  the  lifter  (Fig.  37), 
and  lower  it  gently  till  the  pin  floats  on  the  water,  then  remove 
the  lifter.  If  the  pin  sinks  now  or  later  in  the  experiment,  take 
it  out  with  the  lifter,  wipe  it  dry  with  the  fingers  (which  leaves 
it  somewhat  oily),  and  try  again.  Observe  closely  the  shape  of 
the  water  about  the  pin.  Describe  it,  and  draw  an  enlarged  figure 
of  a  cross  section  of  the  pin  and  adjacent  water  surface,  taken 
at  right  angles  to  the  length  of  the  pin. 

Push  the  pin  till  it  breaks  through  the  surface.  Why  does  it 
sink  now  ?  Why  did  it  float  before  ? 

b.  Float  two  wooden   toothpicks  on  the  water,  placing   them 
parallel   and  about  2  cm.  apart.      (Pins  can  be    used,  but  it  is 
difficult  to  keep  them  afloat.)     Dip  the  glass  rod  into  the  alcohol, 
and  carry  a  drop  on  the  end  of  it  to  the  surface  of  the  water  be- 
tween the  toothpicks.     What  happens  ?     The  alcohol,  mixing  with 
the  water  between  the  toothpicks,  weakens  the  surface  tension. 
How  does  this  account  for  the  behavior  of  the  toothpicks? 

Repeat  the  experiment,  using  the  rubber  band  instead  of  the 
toothpicks,  and  drop  the  alcohol  inside  the  band. 

Similar  results  would  be  obtained  if  oil  were  used  in  these  ex- 
periments, instead  of  alcohol ;  but  it  would  be  necessary  to  change 
the  water  after  each  trial.  Why  ? 

c.  Dip  the  wire  ring  into  the  soap  solution,  and  withdraw  it 
obliquely.     Repeat  if  necessary,  till  a  film  is  obtained.     Observe 
the  behavior  of  the  loose  thread  as  it  floats  in  the  film.     With 
the  point  of  a  pencil,  break  the  film  on  one  side  of  the  thread. 
Describe  and  account  for  the  behavior  of  the  thread.     Draw  a 
figure  showing  the  position  it  takes  with  a  film  on  only  one  side 
of  it. 

d.  What  is  the  shape  of  the  oil  globule  suspended  in  the  mix- 
ture of  alcohol  and  water?     What  gives  it  this  shape?     Disturb 
the  drop  by  tipping  the  bottle  slightly  from  side  to  side,  but  not 
so  quickly  as  to  break  the  drop.     When  the  drop  is  distorted  by 
this  motion,  does  it  recover  its  former  shape?     Account  for  this 
behavior. 


QO  •         MOLECULAR   PHENOMENA 

Experiment  46.  To  study  capillary  action  with  reference  to  the 
effect  of  the  size  of  the  tubes  and  the  direction  of  the  curvature  of  the 
liquid. 

Apparatus.  —  Capillary  tubes  of  glass  of  different  sizes  ;  capillary 
tubes  coated  inside  with  paraffine  ;  glass  of  water ;  glass  containing 
mercury. 

[To  coat  a  tube  with  paraffine,  put  a  very  small  piece  of  paraffine 
in  one  end  of  the  tube,  and  hold  it  obliquely  in  a  flame  till  the 
paraffine  melts  and  runs  down  the  tube.] 

Experimental  Work.  —  a.  Observe  the  shape  of  the  water  and 
mercury  surfaces  near  the  glass.  Draw  figures  of  vertical  sections 
through  the  liquids,  to  illustrate.  Account  for  the  difference  in 
the  shape  of  the  two  surfaces. 

b.  In  the  following  work  use  one  set  of  capillary  tubes  in  water 
only  and  the  other  set  in  mercury  only.     Place  tubes  of  different 
sizes  in  the  tumbler  of  water.     Make  a  section  drawing  of  the 
tumbler   and  tubes,  showing   the   height  of   the  water   and   the 
shape  of  its  surface  in  the  tumbler  and  in  the  tubes.     How  does 
the  diameter  of  a  tube  affect  the  height  to  which  water  rises  in 
it  above  the  level  in  the  tumbler?     How  is  the  water  raised  and 
sustained  in  the  tubes? 

c.  Repeat  the  preceding  with  tubes  of  different  sizes  in  mer- 
cury, using  only  dry  tubes.      By  pressing  the    tube   against  the 
side  of  the  tumbler  an  unobstructed  view  of  the  inside  of  the 
tube  will  be  obtained.     Describe  what  is  seen  and  make  a  section 
drawing  to  illustrate. 

d.  Place  in  the  tumbler  of  water   the    capillary  tube   coated 
on  the  inside  with  paraffine.     Is  the  water  in  the  tube  elevated 
above  or  depressed  below  the  level  of  the  water  in  the  tumbler? 
Is  the  surface  of  the  water  in  the  tube  convex  or  concave  ? 

Discussion.  —  Is  the  liquid  in  a  capillary  tube  elevated  or 
depressed  when  the  surface  of  the  liquid  is  concave?  when  the 
surface  is  convex?  State  the  reason  in  each  case. 


VII.    HEAT 

EXERCISE   25.     CONDUCTION   AND   CONVECTION 

References. — Adams,  374-379  ;  Coleman,  215-218;  Car.  & 
C-,  343-349;  Ches-  G-  &  T->  213-216;  Hoad.  Br.,  253-256; 
Hoad.  El.,  271-276;  Mumper,  140-142;  Mil.  &  G.,  291-297  ; 
Went.  &  H.,  115-120. 

Experiment  47. —  To  determine  the  order  in  which  glass  and 
different  metals  stand  as  conductors  of  heat. 

Apparatus.  —  Rods  of  brass,  iron,  copper,  and  glass  (about 
No.  9  or  10  wire)  ;  Bunsen  burner;  vessel  of  water ;  test  tube. 

Experimental  Work.  —  Test  the  relative  conductivity  of  the 
rods,  two  at  a  time,  holding  one  in  each  hand,  with  an  end  of 
each  in  the  Bunsen  flame  6  or  8  cm.  above  the  burner,  the  two 
being  as  nearly  as  possible  equally  heated.  At  first  hold  the  rods 
near  the  heated  end  ;  then,  as  they  became  uncomfortably  hot, 
hold  them  farther  from  this  end,  observing  in  which  the  heat 
travels  faster.  The  method  may  be  varied  by  holding  the  rods 
at  the  same  distance  from  the  heated  end,  and  observing  in  which 
the  heat  first  reaches  the  hand. 

Before  trying  the  same  rod  a  second  time,  it  may  be  cooled  in 
the  vessel  of  water,  except  the  glass  rod,  which  must  be  allowed 
to  cool  of  itself,  for  it  will  break  if  thrust  into  the  water  hot. 
Continue  experimenting  till  you  can  arrange  the  rods  in  the  order 
of  their  conductivity.1  Write  the  names  in  order,  from  the  best  to 
the  poorest  conductor. 

1  The  rise  of  temperature  along  the  rods  depends  upon  another  property 
of  the  substances  besides  their  conductivity.  This  property,  called  specific 
heat,  will  be  studied  later.  It  does  not  affect  the  order  of  conductivity  of  the 
materials  used  in  this  experiment. 

91 


HfiAf 


b.  Fill  the  test  tube  with  water  within  2  or  3  cm.  of  the  top. 
Hold  it  at  the  bottom  in  the  fingers,  tipping  it  slightly,  and  apply 

the    Bunsen     flame     a     little 
/          below  the    top   of  the   water 
'  If   )     (Fig-   39),  till  it  boils  at  the 
^^J        top  for  about  a  minute. 

What  do  you  observe  con- 
cerning the  temperature  of 
the  water  at  the  bottom  of 
the  tube?  What  do  you  con- 
clude concerning  the  conduc- 
tivity of  water  ? 

Experiment  48.  To  observe  whether  sensations  of  heat  and  cold 
are  affected  by  the  conductivity  of  the  substances  touched. 

Apparatus.  —  Two  pieces  each  of  several  of  the  following  sub- 
stances :  brass,  iron,  glass,  copper,  wool,  asbestos,  stone,  and  wood ; 
hot  air  bath ;  ;ice  box  (unless  the  weather  is  cold). 

Experimental  Work.  —  a.  Place  one  set  of  the  substances  in 
the  air  bath  and  apply  a  low  flame  for  several  minutes.  Place  the 
other  set  in  the  ice  box,  or,  if  the  weather  is  cold,  in  the  open  air 
outside  a  window.  After  five  minutes  or  more,  when  all  the  sub- 
stances in  the  bath  have  had  time  enough  to  come  to  the  same 
temperature  (the  temperature  of  the  bath),  grasp  them  in  the 
hand,  one  at  a  time,  without  removing  them  from  the  oven,  and 
note  the  temperature  sensation.  Repeat  until  you  can  write  a 
list  of  them  in  order,  beginning  with  the  one  thatfee/s  the  hottest. 
(It  is  incorrect  to  say  that  one  is  hotter  than  another.)  Note 
the  temperature  sensation  due  to  the  hot  air  of  the  bath,  and 
include  air  in  the  list  of  substances.  Account  for  the  seeming 
difference  of  temperatures. 

b.  Try  the  same  substances  cooled  in  the  ice  box  or  outside 
the  window,  and  arrange  a  list  in  order,  beginning  with  the  one 
that  feels  the  coldest.  In  making  this  test  it  is  better  to  press 


RADIANT   ENERGY  93 

the  substances,  two  at  a  time,  against  the  forehead,  which  is  much 
more  sensitive  than  the  hands.  After  testing  any  substance  it 
must  be  allowed  to  cool  again  before  making  a  further  test  of  it. 
Account  for  the  seeming  difference  of  temperatures. 

Experiment  49.  —  To  study  convection  currents  in  water. 

Apparatus. — Test  tube;  Bunsen  burner;  beaker;  sawdust; 
iron  stand  ;  wire  gauze ;  mop  cloth. 

Experimental  Work.  —  a.  Put  a  small  pinch  of  sawdust  in  the 
beaker,  and  fill  it  nearly  full  of  water.  Wipe  the  outside  of  the 
beaker  dry,  place  it  on  the  wire  gauze  on  the  ring  stand,  and  apply 
heat  with  the  Bunsen  flame.  The  gauze  should  be  about  10  cm. 
above  the  burner,  and  the  flame  turned  down  so  that  it  will  not 
burn  above  the  gauze.  Observe  carefully  the  motion  of  the  parti- 
cles of  sawdust  while  the  water  is  heating.  Give  a  full  account 
of  what  is  observed,  including  definite  reasons  for  any  motion  of 
the  liquid  that  you  may  infer  from  the  behavior  of  the  sawdust. 

b.  Fill  the  test  tube  nearly  full  of  water  and  hold  it  in  the  hand 
just  below  the  surface  of  the  water,  and  apply  the  flame  near  the 
bottom.  Note  the  rapidity  of  the  rise  of  temperature  of  the  water 
at  the  top. 

Compare  with  the  experiment  in  conduction,  in  which  the  heat 
was  applied  near  the  top  of  the  tube  and  the  tube  was  held  near 
the  bottom.  Account  for  the  difference  in  the  results  of  the  two 
experiments. 

EXERCISE   26.     RADIANT  ENERGY 

References.  —  Adams,  381-385  ;  Coleman,  219-226  ;  Car.  &  C., 
350,  352-354;  Ches.  G.  &T.,  217  ;  Hoad.  Br.,  258-263  ;  Hoad. 
EL,  280-286;  Mumper,  146-151  ;  Mil.  &  G.,  299-300;  Went.  & 
H.,  121-125. 

Experiment  50.  —  To  study  the  transmission,  absorption,  and 
reflection  of  radiant  energy. 

Apparatus.  —  Bunsen  burner ;  a  bright  tin  screen  about  8  by 
8  in.,  mounted  on  stand  or  supported  by  ring  stand  and  clamp ; 


94  HEAT 

mounted  tin  screen,  same  size,  painted  black  or  coated  with  soot 
on  one  side. 

• 

Experimental  Work.  —  a.  Hold  the  hand  in  different  positions 
near  the  flame,  at  the  side  and  above  it.  Do  you  feel  convection 
currents  in  any  position?  There  may  possibly  be  convection 
currents  that  are  too  weak  to  be  felt  as  currents,  although  they 
warm  the  hand.  Can  you  suggest  any  conclusive  reason  for  be- 
lieving that  the  hand  is  not  warmed  by  such  a  current  when  held 
at  the  side  of  the  flame  ? 

b.  Hold  the  hand  close  beside  the  flame,  and  note  the  intensity 
of  the  sensation.     With  the  hand  still  in  this  position,  insert  a 
sheet  of  paper  between  it  and  the  flame,  and  note  the  effect  on 
the  sensation  of  heat.    How  does  this  effect  prove  that  the  hand 
was  not  heated  by  conduction  through  the  air  from  the  flame  ? 

c.  Place  the  tin  screens  on  opposite  sides  of  the  flame,  at  equal 
distances  of  about  10  cm.  from  it,  with  the  black  side  of  the  one 
turned  toward  the  flame.     After  a  minute  or  two,  note  the  tem- 
perature of  the  screens  by  placing  a  hand  flat  against  each  on  the 
side  turned  from  the  flame.     What  do  you  learn  concerning  the 
temperatures  of  the  two  screens  ?     How  is  this  explained  ? 

d.  Remove  the  bright  screen  and  hold  one  hand  in  its  place  at 
the  same  distance  from  the  flame  as  the  other  hand,  which  is  still 
pressed  against  the  back  of  the  black  screen.      Which  hand  be- 
comes warmer?     Explain. 

e.  What  facts  point  to  the  conclusion  that  the  black   screen 
becomes  much  hotter  than  the  air  at  that  distance  from  the  flame  ? 
Why  is  this? 

Experiment  51.  —  To  find  whether  radiant  energy  is  transmitted 
along  a  straight  path,  and  to  test  the  power  of  different  substances 
to  absorb  and  transmit  luminous  and  non-luminous  radiation. 

Apparatus.  —  Bunsen  burner;  radiometer;  three  flat  bottles  of 
clear  glass,  one  empty,  one  filled  with  water,  and  one  with  a  solu- 
tion of  iodine  in  carbon  bisulphide. 


RADIANT    ENERGY  95 

CAUTION.  Carbon  bisulphide  is  dangerously  inflammable.  The 
bottle  must  be  kept  tightly  corked  and  must  be  handled  with  care. 
It  should  be  provided  with  a  support  to  avoid  danger  of  over- 
turning. 

Experimental  Work.  — a.  Place  the  radiometer  at  different  dis- 
tances from  the  flame,  and  observe  the  effect  of  distance  upon  the 
rate  of  rotation  of  the  vanes.  Radiation,  both  luminous  and  non- 
luminous,  falling  upon  the  radiometer,  will  cause  the  vanes  to  ro- 
tate ;  and  the  rate  of  rotation  is  an  indication  of  the  intensity  of 
the  radiation. 

b.  Place  the   radiometer  about   30  cm.   from  the    flame  and 
slowly  insert  a  sheet  of  paper  or  a  book  between  them.     What  is 
the  position  of  the  screen  when  the  slower  rotation  of  the  vanes 
indicates  that  the  radiation  has  been  cut  off  from  the  radiometer? 
Does  the  effect  of  the  screen  indicate  that  radiant  energy  is  or  is 
not  transmitted  along  a  straight  path  ? 

c.  Hold  the  empty  flask  between  the  flame  and  the  radiometer, 
and  bring  the  latter  up  till  the  vanes  make  about  one  rotation  per 
second.     Now  remove  the  flask  and  note  the  effect  on  the  radiom- 
eter.    What  do  you  infer  in  regard  to  the  power  of  clear  glass 
to  absorb  radiant  energy? 

d.  Without  moving  the  radiometer  or  the  flame,  hold  the  flask 
of  water  between  them.     Compare  the  result  with  that  obtained 
with  the  empty  flask.     A  more  definite  comparison  may  be  made 
by  observing  the  time  of,  say,  ten  rotations ;   but  where  there  are 
easily  observable  differences,  this  is  not  necessary. 

Is  water  a  good  or  poor  absorber  of  luminous  radiation?  (Is  it 
transparent?)  Does  the  action  of  the  radiometer  show  that  water 
is  a  good  or  poor  absorber  of  non-luminous  radiation?  (Probably 
more  than  95  %  of  the  energy  radiated  from  the  flame  is  of  the 
non-luminous  variety.) 

e.  Substitute  the  flask  containing  the  solution  of  iodine  in  car- 
bon bisulphide.     Compare  the  results  with  the  preceding.     Does 
the  solution  transmit  light  (luminous  radiation)  ?     What  evidence 


96  HEAT 

is  there  that  it  transmits  non-luminous  radiation?  Is  it  a  better  or 
poorer  transmitter  of  non-luminous  radiation  than  water  ?  better 
or  poorer  than  glass? 

EXERCISE  27.    COEFFICIENT  OF  LINEAR  EXPANSION 

References.  —  Adams,  351;  Coleman,  233;  Car.  &  C.,  319; 
Ches.  G.  &  T.,  220-221  ;  Hoad.  Br.,  264-265  ;  Hoad.  EL,  287- 
288;  Mumper,  113-114;  Mil.  &  G.,  197;  Went.  &  H.,  96. 

Experiment  52.  —  To  find  the  expansion  of  i  cm.  of  a  brass 
rod  due  to  a  rise  of  temperature  of  i°. 

Apparatus.  —  Linear  expansion  apparatus  (Fig.  40)  ;  apparatus 
for  generating  steam;  tumbler;  meter  rod;  Bunsen  burner; 
access  to  a  thermometer.  ' 


FIG.  40. 

[For  the  steam  generator  use  a  copper  boiler  on  tripod,  with  a 
tight  top,  or  flask  with  stopper  and  delivery  tube,  supported  on 
a  ring  stand.] 

Experimental  Work.  —  a.  Fill  the  steam  generator  from  one 
third  to  one  half  full  of  water,  and  with  the  top  off  (or  the  delivery 
tube  disconnected  at  the  generator)  begin  heating  it.  While  the 
water  is  heating,  measure  the  length  of  the  brass  rod  without 
removing  it  from  the  steam  jacket ;  then  adjust  it  so  that  one 
end  rests  against  the  fixed  support  and  the  other  against  the  lever. 
Turn  it  so  that  the  escape  tube  will  be  directed  downward.  4  Set 
the  tumbler  under  this  tube  to  catch  the  escaping  steam  and  hot 
water. 

b.  Read  to  .1  mm.  the  position  of  the  long  lever  arm  on  the 
vertical  scale.  After  taking  this  reading,  be  careful  not  to  disturb 


COEFFICIENT   OF   LINEAR   EXPANSION  97 

the  apparatus  in  any  way,  as  this  would  probably  move  the  lever 
into  a  new  position. 

c.  The  temperature  of  the  rod  is  the  same  as  that  of  the  room. 
Find  it  by  the  laboratory  thermometer. 

d.  Put  the  top  on  the  steam  generator  and  connect  the  delivery 
tube.     While  the  rod  is  being  heated  by  the  steam,  observe  the 
motion  of  the  long  lever  arm.     After  the  steam  has  been  escaping 
freely  from  the  escape  tube  for  two  or  three  minutes  and  no  further 
motion  of  the  lever  can  be  detected,  read  the  position  of  the  long 
lever  arm.     The  temperature  of  the  rod  is  the  same  as  the  tem- 
perature of  the  steam,  which  may  be  assumed  to  be  100°. 

e.  Measure   the   arms  of  the   lever.     These  are  the  distances 
from  the  fulcrum  (a  knife  edge  or  the  center  of  a  screw)  to  the 
scale  and  from  the  fulcrum  to  the  point  of  contact  with  the  brass 
rod,  respectively.     When  you  have  finished,  tilt  the  apparatus  so 
that    the    water    con- 
densed  in   the   steam 

jacket  will  run  out. 

Data  and  Computa- 
tions.—  The  whole  ex- 
pansion of  the  rod  is 

the   distance   //x   (Fig.  FIG.  41. 

41)  that  the  short  arm 

of  the  lever  is  pushed  forward.  Compute  this  from  the  pro- 
portion d±  :  d>2  : :  a±  :  a2.  Record  data  and  computations  as 
follows  :  — 

MEASUREMENTS 

Length  of  brass  rod  =  cm. 

First  position  of  long  lever  arm  =  cm. 

First  temperature  of  the  rod  =  °  C. 

Final  temperature  of  the  rod  °  C. 

Final  position  of  long  lever  arm  —  cm. 

Length  of  long  lever  arm  a2  —  cm. 

Length  of  short  lever  arm  a±  =  cm. 
COLEMAN'S  NEW  MANUAL  —  7 


98  HEAT 

COMPUTATIONS 

Rise  of  pointer  on  the  index,  d^  =  cm. 
Change  of  temperature  of  the  rod  °  C. 
Expansion  of  rod  for  this  change  of  temperature,  d±  =  cm. 
Expansion  of  rod  for  i°  change  of  temperature  =       cm. 
Expansion  of  i  cm.  of  rod  for  i°  change  of  temper- 
ature (coefficient  of  linear  expansion  of  rod)  =  cm. 
True  value  of  coefficient  of  expansion  of  brass  =  .0000188 
Percentage  of  error  =  % 

ALTERNATIVE  DIRECTIONS 

If  the  apparatus  is  provided  with  a  micrometer  screw  instead  of 
a  lever,  the  following  substitutions  are  to  be  made  in  the  directions 
as  given  above  :  — 

b.  If  you  do  not  know  how  to  read  the  micrometer  screw,  turn 
it  back  and  forth  and  study  its  action.  Note  the  fixed  milli- 
meter scale  and  the  circular  scale  on  the  head ;  also  that  when 
the  head  is  turned  once  round,  it  advances  i  mm.  along  the  fixed 
scale.  How  many  divisions  are  there  on  the  circular  scale  ?  The 
value  of  one  division  on  the  circular  scale  is  the  distance  the  screw 
advances  when  the  head  is  turned  through  one  division.  What  is 
this  value  ?  Ask  for  assistance  if  necessary.  The  answers  to  these 
questions  need  not  be  recorded. 

See  that  the  other  end  of  the  rod  is  against  the  fixed  support, 
then  turn  the  micrometer  screw  till  it  just  touches  the  rod,  and 
take  its  reading.  After  taking  the  reading,  turn  the  screw  back 
2  or  $  mm.  to  make  room  for  the  expansion  of  the  rod  when  heated 
If  this  precaution  is  not  observed,  the  expanding  rod  will  strain 
and  damage  the  apparatus.  Observe  the  additional  precautions 
given  in  paragraph  b  above. 

d.  In  this  paragraph  substitute  for  the  reading  of  the  lever  a 
second  reading  of  the  screw,  after  it  has  been  turned  up  to  touch 
the  rod.  The  difference  between  the  two  readings  of  the  screw  is 
the  expansion  of  the  rod. 


COEFFICIENT   OF   EXPANSION   OF   AIR  99 

EXERCISE   28.     COEFFICIENT  OF  EXPANSION  OF  AIR 

References.  —  Adams,  352-353;  Coleman,  237;  Car.  &  C., 
318-320;  Ches.  G.  &T.,  223;  Hoad.  Br.,  268-269;  Hoad.  EL, 
293-295  ;  Mumper,  118;  Mil.  &  G.,  191  ;  Went.  &  H.,  97. 

Experiment  53. —  To  find  whether  the  expansion  of  air  is  uni- 
form, and  to  find  by  what  fraction  of  its  volume  at  o°  air  expands 
when  its  temperature  is  raised  i°. 

Apparatus.  —  Copper  steam  generator  with  tall  top ;  Bunsen 
burner ;  hydrometer  jar ;  stirrer  of  wire  bent  into  a  flat  coil  at  the 
end  ;  thermometer ;  glass  tube  containing  air  and  mercury  index ; 
metric  rule ;  ice. 

[The  tube  containing  air  must  be  of  small  bore  (not  greater 
than  i  mm.),  in  order  to  hold  the  mercury  index  in  position,  and 
should  be  35  to  40  cm.  long.  Prepare  as  follows  :  Thoroughly 
dry  the  tube  by  warming  it  and  passing  through  it  air  that  has  first 
passed  through  a  calcium  chloride  drying  tube.  Insert  an  end 
of  the  tube  into  clean  mercury,  withdraw  a  column  about  2  cm. 
long,  and  let  it  run  some  distance  down  the  tube.  Seal  an  end  of 
the  tube  in  a  flame,  then  work  the  index  into  proper  position  with 
a  fine  wire,  leaving  the  confined  air  column  about  two  thirds  the 
length  of  the  tube.] 

Method.  —  The  thread  of  mercury  in  the  glass  tube  serves  as  an 
air-tight  piston  to  confine  a  fixed  mass  of  air  between  it  and  the 
closed  end  of  the  tube. 

Since  the  tube  is  of  uniform  bore,  the  volume  of  this  confined 
air  is  proportional  to  its  length.  This  length  is  determined  when 
the  tube  is  surrounded  by  melting  ice,  when  it  is  immersed  in 
warm  water,  and^  when  immersed  in  steam.  The  tube  is  in  each 
case  vertical,  with  the  open  end  up,  when  the  measurements  are 
taken ;  hence  the  confined  air  is  under  a  constant  pressure  (the 
pressure  of  the  atmosphere  plus  the  pressure  due  to  the  weight  of 
the  mercury  index). 


1 00  HEAT 

Experimental  Work.  —  Handle  the  tube  carefully ;  a  sudden 
motion  might  break  the  thread  of  mercury,  and  this  must  be 
avoided.  Measure  accurately  the  total  length  of  the  bore  of  the 
tube  (i.e.  the  distance  from  the  open  end  to  the  inside  of  the 
closed  end),  and  the  length  of  the  mercury  index. 

Place  the  tube,  open  end  up,  in  the  hydrometer  jar,  and  fill  the 
jar  with  crushed  ice  or  snow  up  to  the  index.  While  waiting  a 
minute  or  two  for  the  tube  to  come  to  the  temperature  of  the  ice, 
fill  the  steam  generator  about  two  thirds  full  of  water  and  begin 
heating  it.  With  the  tube  still  in  the  ice,  tap  it  very  lightly  to 
jar  the  index  into  its  true  position,  then  measure  the  distance 
from  the  top  of  the  index  to  the  top  of  the  tube.  Subtracting  this 
distance,  together  with  the  length  of  the  mercury  index,  from  the 
total  length  of  the  bore  of  the  tube  gives  the  length  of  the  confined 
air  column.  Its  length  at  the  other  temperatures  is  found  in  the 
same  way. 

Remove  the  tube,  pour  the  water  from  the  jar,  and  return  the 
remaining  ice  to  the  supply  vessel.  Fill  the  jar  with  water  from 
the  faucet,  and  let  it  stand  a  moment  to  warm  the  jar,  then  empty 
and  fill  with  water  at  35°  to  40°  from  the  supply  that  is  being 
heated.  Be  careful  not  to  pour  hot  water  into  the  jar ;  if  thick 
glass  is  heated  suddenly,  it  will  break.  Stir  the  water  in  the  jar 
thoroughly  by  moving  the  stirrer  repeatedly  from  top  to  bottom 
of  the  jar ;  place  the  tube  and  thermometer  in  it ;  take  the 
temperature  accurately ;  and  after  tapping  the  tube  lightly,  meas- 
ure the  distance  from  the  top  of  the  index  to  the  top  of  the 
tube. 

Place  the  top  on  the  steam  generator,  and  boil  the  water.  Push 
the  tube  through  the  hole  in  the  cork  which  closes  the  top  of  the 
generator,  and  push  it  farther  down  as  the  index  rises  in  the  tube, 
until  finally  the  index  appears  just  above  the  cork  when  it  has 
become  stationary.  After  the  steam  has  been  escaping  from  the 
vent  for  some  time  and  the  index  has  ceased  to  rise,  measure 
';he  distance  frou  the  top  of  the  index  to  the  top  of  the  tube. 

Leave  the  tube  standing  in  the  empty  hydrometer  jar. 


SPECIFIC  HEAT  IOI 

Data  and  Computations.  —  Record  data  as  follows,  and  perform 
the  indicated  computations  :  — 

MEASUREMENTS 

Total  length  of  bore  of  tube  =  cm. 

Length  of  mercury  index  =  cm. 
Distance  from  top  of  index  to  top  (open  end)  of  tube 

when  tube  is  in  ice  (temp.  o°  C.)  =  cm. 

when  tube  is  in  water  at °  C.     (This  tem- 
perature is  denoted  below  by  /°)  =  cm. 

when  tube  is  in  steam  (temp.  100°)  =  cm. 

COMPUTATIONS 

Length  of  air  column  at  o°  =  cm. 

Length  of  air  column  at  /°  (temp.. in  water)  =  cm. 

Length  of  air  column  at  100°  =  cm. 
Average  expansion  of  air  column  per  degree 

rise  of  temperature 

between  o°  and  /°  =  cm. 

between  /°  and  100°  =  cm. 

between  o°  and  100°  =  cm. 
Computed  coefficient  of  expansion  between  o° 

and  100°  =  cm. 

True  value  of  coefficient  of  expansion  of  air  =  .00366 

Percentage  of  error  =  % 

Discussion.  —  What  information  do  your  results  afford  on  the 
question  whether  the  expansion  of  air  is  uniform  within  the  tem- 
perature limits  of  the  experiment  ? 

EXERCISE    29.     SPECIFIC   HEAT 

References.  —  Adams,  369,  371-373;  Coleman,  239-243;  Car. 
&C.,  325-328;  Ches.  G.  &  T.,  226-230;  Hoad.  Br.,  281-283; 
Hoad.  EL,  312-314,  316;  Mumper,  110-112;  Mil.  &  G.,  239, 
250-251  ;  Went.  &  H.,  107-109.  . 


102  HEAT 

Experiment  54.  —  To  find  the  number  of  calories  required  to 
raise  the  temperature  of  i  g.  of i°. 

Apparatus.  —  Bunsen  burner ;  copper  vessel  on  tripod,  or  other 
open  vessel  for  boiling  water;  open  roll  (Fig.  42)  or  other  mass 
of  metal,  with  fine  wire  attached  for  handle ;  calorimeter ;  ther- 
mometer ;  platform  balance  and  weights  to  500  g. ;  mop  cloth. 

[The  piece  of  metal  whose  specific  heat  is  to  be  found  should 
weigh  from  250  to  400  g.     A  sphere  or  other  compact  mass  will 
serve;   but  an  open  roll  of  sheet   metal   i   to  2   mm.  thick   is 
better.     The  space  between  the  surfaces 
of  the  roll  must  be  wide  enough  to  avoid 
holding  water    by  capillary  action.      A 
light   calorimeter    of  thin    nickel-plated 
brass  or  of  aluminum  is  preferable ;  but 
a  glass  beaker  or  even  a  small  tin  can  will 
serve.     It  makes  a  rather  better  experi- 
ment to  find  the  specific  heat  of  the  metal 
of  which  the  calorimeter  is  made,  using 
FIG.  42.  a  roll  or  other  mass  of  the  same  metal.] 

Experimental  Work.  —  Begin  heating  water  in  the  copper  boiler. 
Weigh  the  piece  of  metal  whose  specific  heat  is  to  be  found. 

Weigh  the  calorimeter.  Put  the  roll  into  the  calorimeter,  and 
pour  in  enough  water  to  cover  it.  The  water  should  be  about  3° 
below  the  temperature  of  the  room,  for  best  results.  Put  the  roll 
into  the  water  that  is  being  heated,  and  see  that  there  is  enough 
water  in  the  boiler  to  cover  it.  Weigh  the  calorimeter  and  the 
water  in  it. 

After  the  above  has  been  done  and  the  water  in  the  vessel  is 
boiling,  thoroughly  stir  the  water  in  the  calorimeter  with  the  ther- 
mometer and  take  its  temperature  to  a  tenth  of  a  degree.  (The 
temperature  must  be  read  as  accurately  as  possible.  An  error  of .  i° 
in  determining  a  temperature  change  of  5°  is  an  error  of  5  %.) 

As  soon  as  the  temperature  is  taken,  remove  the  thermometer, 
hold  the  calorimeter  close  beside  the  boiler,  and  transfer  the  roll 


SPECIFIC   HEAT  1 03 

to  the  calorimeter  as  quickly  as  possible.  (It  is  assumed  that  the 
temperature  of  the  roll  is  100°  when  it  is  put  into  the  calorimeter  ; 
but  it  cools  with  great  rapidity  during  the  transfer,  and  a  delay 
of  even  a  second  will  cause  a  considerable  error  in  the  result.) 
Place  the  calorimeter  on  the  table  at  a  distance  from  the  flame, 
move  the  roll  about  in  it  to  stir  the  water,  then  insert  the  ther- 
mometer and  take  the  temperature  near  the  top  and  the  bottom 
of  the  water  and  on  opposite  sides  of  the  roll.  If  differences  are 
found,  stir  again.  Record  the  highest  uniform  temperature. 

If  time  permits,  the  experiment  should  be  repeated.  Having 
become  familiar  with  the  method  of  procedure,  you  will  very  prob- 
ably secure  better  results.  Leave  the  calorimeter  empty. 

Data  and  Computations.  —  Let  s  denote  the  specific  heat  of  the 
roll.  If  the  calorimeter  is  of  the  s^ame  metal  as  the  roll,  its  spe- 
cific heat  is  also  denoted  by  s.  That  is,  s  denotes  the  number  of 
calories  lost  by  each  gram  of  the  roll  as  its  temperature  falls  one 
degree,  and  also  the  number  of  calories  received  by  each  gram 
of  the  calorimeter  as  its  temperature  rises  one  degree.  If  the 
calorimeter  and  the  roll  are  of  different  metals,  the  specific 
heat  of  the  calorimeter  is  treated  as  a  known  quantity  in  the  com- 
putations, and  its  value  is  taken  from  a  table  of  specific  heats. 

The  calorimeter  is  assumed  to  be  at  the  temperature  of  its  con- 
tents. The  heat  gained  by  the  water  and  the  calorimeter  is 
assumed  to  come  entirely  from  the  roll  (any  transfer  of  heat  be- 
tween the  vessel  and  outside  bodies  is  disregarded)  ;  i.e. 

Heat  lost  by  roll  =  heat  received  by  water 

-f  heat  received  by  calorimeter. 

The  algebraic  statement  of  this  relation  (i.e.  with  the  quantities 
expressed  numerically  or  algebraically)  is  called  the  heat  equation. 
The  specific  heat  is  found  by  solving  this  equation  for  s. 

Be  careful  to  specify  in  the  record  what  metal  is  used  in  the 
experiment  and  of  what  metal  the  calorimeter  is  made.  Record 
as  follows  :  — 


104  HEAT 

Weight  of  roll  of =       g. 

Weight  of calorimeter  =       g. 

Weight  of  calorimeter  and  water  =       g. 

Initial  temperature  of  water  and  calorimeter  =       °  C. 

Initial  temperature  of  roll  of-  =100°  C. 

Final  temperature  of  calorimeter  and  contents  =       °  C 

COMPUTATIONS 

Weight  of  water  used  =       g. 
Rise  of  temperature  of  water  and  calorimeter 

Heat  received  by  water  =       cal. 

Heat  received  by  calorimeter  =()x()XJ  =       cal. 

Fall  of  temperature  of  roll  =       ° 

Heat  given  out  by  roll  =()x()XJ  —       cal. 
Heat  equation  and  its  solution  :  — 

Computed  specific  heat  of ,  s  = 

True  value  of  the  specific  heat  = 

Percentage  of  error  =        % 

EXERCISE   30.     MELTING  AND   FREEZING 

References.  —  Adams,  386-388  ;  Coleman,  231,  244-247  ;  Car. 
&  C.,  311,  329-332;  Ches.  G.  &T.,  207,  232-237;  Hoad.  Br., 
240,  271-273;  Hoad.  El., -257,  298-300;  Mumper,  105,  122- 
123  ;  Mil.  &  G.,  180,  264-269,  273  ;  Went.  &  H.,  94,  99-101. 

Apparatus.  —  Thermometer,  numbered  for  identification  ;  tum- 
bler or  beaker  ;  test  tube  ;  supply  of  ice  and  salt. 

Experiment  ^.  — To  find  the  error  of  the  zero  point  on  a 
thermometer  scale. 

Experimental  Work.  —  a.  Fill  the  beaker  about  half  full  of  fine 
crushed  ice.  Insert  the  thermometer,  and  pack  the  ice  about  it 
nearly  to  the  zero  of  the  scale.  After  the  mercury  ceases  to  fall, 
take  the  temperature  to  .1°.  Record  the  number  of  the  ther- 
mometer and  its  reading  in  melting  ice.  The  graduation  of 
thermometers,  except  expensive  ones,  may  be  in  error  by  several 


MELTING  AND   FREEZING  10$ 

• 

tenths  of  a  degree.  The  temperature  of  melting  ice  (when  by 
itself)  is  exactly  zero.  The  reading  of  a  centigrade  thermometer 
in  melting  ice  is  therefore  the  error  of  its  zero  point. 

b.  What  evidence  is  there  that  the  ice  you  used  was  melting? 
Was  the  ice  receiving  or  losing  heat  during  the  experiment? 
How  and  why? 

Experiment  56. —  To  find  whether  freezing  and  melting  take 
place  at  the  same  temperature. 

Experimental  Work.  —  a.  Mix  with  the  ice  in  the  beaker  about 
one  fourth  its  volume  of  table  salt.  Put  enough  water  into  the 
test  tube  to  cover  the  bulb  of  the  thermometer  when  inserted  in 
it,  and  place  it  in  the  freezing  mixture  of  salt  and  ice.  Stir  the 
water  in  the  test  tube  with  the  thermometer,  keeping  watch  of 
its  temperature.  At  what  temperature  does  it  begin  to  freeze? 
Continue  the  stirring  and  take  the  temperature  from  time  to  time 
as  the  freezing  continues.  What  is  the  reading  of  the  thermometer 
in  freezing  water  ?  How  do  the  temperatures  of  melting  ice  and 
freezing  water  compare? 

b.  After  a  third  or  a  half  of  the  water  in  the  tube  is  frozen,  allow 
the  remainder  to  freeze  round  the  bulb  of  the  thermometer.  What 
change  of  temperature  do  you  observe  after  the  water  is  all  frozen? 

To  free  the  thermometer  from  the  ice,  let  water  from  the  faucet 
run  on  the  test  tube.  Take  the  temperature  of  the  freezing  mix- 
ture. Was  the  water  in  the  test  tube  receiving  or  losing  heat 
while  it  was  freezing?  Why? 

Experiment  57.  —  To  observe  the  effect  of  pressure  upon*  the 
melting  point  of  ice. 

Apparatus.  —  A  block  of  ice  supported  at  the  ends ;  a  heavy 
weight  suspended  from  the  block  of  ice  by  means  of  a  loop  of 
fine  wire  passed  over  it. 

[The  most  convenient  procedure  with  this  experiment  is  for  the 
teacher  to  set  it  up,  at  or  just  before  the  beginning  of  the  labora- 
tory period,  and  have  all  the  members  of  the  class  observe  its 
progress  from  time  to  time  during  the  hour.] 


IO6  HEAT 

• 
Experimental  Work.  —  a.   When  the  weight  was  hung  upon  the 

ice,  the  wire  rested  upon  its  surface.     How  do  you  find  it  now? 

Look  at  it  from  time  to  time  during  the  hour,  and  note  any  change 

in  the  position  of  the  wire. 

b.    How  is  the  cut  that  the  wire  makes  in  the  ice  mended  ? 

What  is  the  cause  of  the  melting  under  the  wire?     What  is  the 

source  of  the  heat  required  for  this  melting?     Why  does  the  water 

above  the  wire  freeze?     (Heat  received  by  the  ice  from  the  air 

and  other  bodies  does  not  reach  the  interior.) 

EXERCISE    31.      HEAT    OF    FUSION    AND    SOLUTION 

References.  —  Adams,  389-392  ;  Coleman,  248-250 ;  Car.  & 
C.,  332-334;  Ches.  G.  &  T.,  238-240;  Hoad.  Br.,  284;  Hoad. 
EL,  315  ;  Mumper,  124-125  ;  Mil.  &  G.,  264-265,  281  ;  Went.  & 
H.,  i  lo-m. 

Experiment  58.  —  To  find  the  number  of  calories  required  to 
change  i  g.  of  ice  at  o°  into  water  at  o°. 

Apparatus.  —  Calo- 
rimeter  ;  thermometer 
and  stirrer  (Fig.  43)  ; 
FlG    3  platform  balance  and 

weights    to    500    g. ; 
cloth ;  ice  plane ;  supply  of  ice  and  of  hot  water. 

[For  a  stirrer  use  a  piece  of  very  thin  sheet  copper  about 
i  x  1.5  in.,  with  two  holes  large  enough  to  slip  it  on  the  end 
of  the  thermometer.] 

Experimental  Work.  —  Weigh  the  calorimeter  to  .1  g.  Put  into 
it  about  150  g.  of  water  at  a  temperature  between  45°  and  50°. 
Take  hot  water  from  the  supply  and  add  cold  water  till  the  tem- 
perature is  right.  Weigh  the  calorimeter  and  water.  During  the 
remainder  of  the  experiment  the  calorimeter  should  stand  on  wood 
or  paper  (poor  conductors),  and  should  be  touched  by  the  hands 
as  little  as  possible. 


HEAT  OF  FUSION  AND   SOLUTION  IO/ 

Have  at  hand  a  quantity  of  shaved  or  crushed  ice.  This  must 
be  dry.  (Why?)  It  is  best  prepared  by  shaving  it  with  an  ice 
plane  immediately  before  using  it.  The  quantity  required  will 
have  a  volume  about  equal  to  the  volume  of  water  used.  If  a 
supply  of  crushed  ice  is  provided,  dry  it  as  much  as  possible  by 
spreading  it  out  on  a  cloth  and  wiping  each  piece  with  a  corner 
of  the  cloth. 

Thoroughly  stir  the  water  in  the  calorimeter  with  the  stirrer  on 
the  thermometer,  and  take  the  temperature  to  .1°.  Immediately 
put  in  nearly  all  of  the  ice,  and  stir  the  water  constantly  while  the 
ice  is  melting.  If  ice  remains  after  the  temperature  has  fallen  to 
about  8°,  remove  it  with  the  stirrer ;  if  the  ice  is  all  melted  before 
the  temperature  has  fallen  to  10°  or  12°,  add  more  without  delay. 
As  soon  as  the  temperature  has  fallen  to  about  8°  and  no  ice 
remains  in  the  calorimeter,  stir  the  water  thoroughly  and  take  the 
temperature  at  top  and  bottom.  If  there  is  a  difference,  stir  and 
read  again.  Record  the  lowest  uniform  temperature  of  the  water. 

Weigh  the  calorimeter  and  contents.  Leave  the  calorimeter 
empty,  and  the  table  dry. 

Data  and  Computations.  —  The  experiment  is  planned  so  that 
the  heat  lost  from  the  calorimeter  and  contents  by  radiation  and 
conduction  while  they  are  warmer  than  the  air  is  approximately 
balanced  by  the  heat  gained  by  the  same  means  after  they  have 
become  colder  than  the  air.  We  may  therefore  assume  that  the 
heat  received  by  the  ice  in  melting  and  the  heat  received  by  the 
ice  water  in  warming  to  the  final  temperature  comes  entirely  from 
the  warm  water  and  the  calorimeter,  and  that  the  heat  received 
by  the  ice  and  the  ice  water  is  equal  to  the  heat  lost  by  the  warm 
water  and  the  calorimeter.  Let /denote  the  heat  of  fusion  of  ice 
(the  number  of  calories  required  to  melt  one  gram  of  ice  without 
change  of  temperature).  Take  the  specific  heat  of  the  calorimeter 
from  the  table  of  specific  heats  in  the  Appendix.  Write  the  heat 
equation  and  solve  it  for  /.  Record  data  and  computations  as 
follows :  — 


108  HEAT 

Weight  of  the  calorimeter  =  g. 

Weight  of  calorimeter  and  water  =  g. 
Temperature  of  calorimeter  and  water  just  before 

adding  ice  =  °  C. 

Final  temperature  of  calorimeter  and  water  =  °  C. 
Final  weight  of  calorimeter  and  water  (including 

water  from  the  ice)  =  g. 

COMPUTATIONS 

Weight  of  water  before  adding  ice  =  g. 

Weight  of  ice  added  =  g. 

Fall  of  temperature  of  calorimeter  and  water  = 

Heat  given  out  by  warm  water  =  cal. 

Heat  given  out  by  calorimeter  =  cal. 

Heat  received  by  the  ice  in  melting  =  (     )  X/  =  cal. 
Heat  received  by  the  ice  water  in  warming  to  the 

final  temperature  =  cal. 
Heat  equation  and  its  solution  :  — 

Computed  heat  of  fusion  of  ice,/  =  cal. 

True  value  of  heat  of  fusion  of  ice  =  79.25  cal. 

Percentage  of  error  °/o 

Experiment  59.  —  To  observe  the  change  of  temperature  when 
ammonium  chloride  or  ammonium  nitrate  is  dissolved  in  water. 

Apparatus.  —  Thermometer;  test  tube;  ammonium  chloride 
or  ammonium  nitrate. 

Experimental  Work.  —  Fill  the  test  tube  about  one  third  full 
of  water  and  take  its  temperature.  Add  a  teaspoonful  or  more 
of  ammonium  chloride  or  ammonium  nitrate,  stir  with  the  ther- 
mometer, and  note  the  change  of  temperature.  What  inference 
may  be  drawn  from  this  change  of  temperature? 

If  there  is  time,  repeat  the  experiment  with  ice-water.  Compare 
the  fall  of  temperature  in  the  two  cases,  and  note  particularly 
whether  the  temperature  falls  below  the  freezing  point  of  pure  water. 


COOLING   BY   EVAPORATION;     DEW-POINT  1 09 

EXERCISE   32.     COOLING   BY   EVAPORATION;  DEW- 
POINT 

References.  —  Adams,  393,  397,  401-403  ;  Coleman,  251-252, 
256-259;  Car.  &  C.,  335-336,  339,  341  ;  Ches.  G.  &  T.,  243- 
249;  Hoad.  Br.,  274-276  ;  Hoad.  El.,  302-305  ;  Mumper,  126- 
127,  134-136;  Mil.  &  G.,  133-143,  145-146;  Went.  &  H.,  102- 
103,  113,  127-128. 

Experiment  60.  —  To  compare  the  rate  of  evaporation  of  water, 
alcohol,  and  ether,  and  to  observe  the  change  of  temperature  due  to 
evaporation. 

Apparatus.  —  Small  bottles  containing  water,  alcohol,  and  ether ; 
thermometer ;  absorbent  cotton. 

Experimental  Work.  —  a.  Pour  a  few  drops  of  water  on  the 
palm  of  the  hand,  and  move  the  hand  back  and  forth  edgewise. 
Note  the  temperature  sensation  and  the  rapidity  with  which  the 
water  evaporates.  Try  the  same  experiment  with  alcohol. 

Compare  the  rapidity  of  evaporation  of  water  and  alcohol  and 
the  temperature  sensations.  Account  for  the  difference  in  the 
temperatures. 

b.  Repeat  the  experiment,  using  ether.     Compare  results  with 
those  obtained  with  water  and  alcohol.     Account  for  the  differ- 
ence in  the  temperatures. 

c.  Take  the  temperature  of  the  air.     Wrap  a  small  quantity  of 
cotton  round  the  bulb  of  the  thermometer,  and  insert  it  in  the 
bottle  of  water.     Take  the  temperature  of  the  water.     Raise  the 
bulb  out  of  the  water,  but  leave  it  still  inside  the  bottle,  and  after 
about  half  a  minute  take    the  temperature.     Remove   the  ther- 
mometer from  the  bottle,  and  observe  any  change  in  the  reading 
as  it  is  held  in  the  air  for  a  short  time.     After  the  temperature 
has  become  constant,  move  the  thermometer  to  and  fro  several 
times,  and   again  read   the  temperature.     Record  the  observed 
temperatures  on  separate  lines. 


110  HEAT 

Account  for  the  equality  of  or  the  difference  between  the 
various  temperatures. 

d.  Replace  the  cotton  on  the  bulb  of  the  thermometer  with  a 
dry  piece,  and  repeat  the  preceding  experiment,  using  ether  in- 
stead of  water. 

Compare  the  results  with  those  obtained  with  water.  Why 
does  the  temperature  cease  to  fall  before  all  the  ether  has  evapo- 
rated from  the  cotton? 

Experiment  61. —  To  find  the  dew-point  of  the  air  in  the 
laboratory. 

Apparatus.  —  Thermometer;  stirrer  of  thin  copper;  bright 
calorimeter ;  two  beakers  ;  ice. 

Experimental  Work.  —  a.  Put  water  in  the  calorimeter  to  a 
depth  of  about  three  centimeters.  Have  at  hand  a  beaker  of 
water,  and  a  small  quantity  of  shaved  or  finely  crushed  ice  in  the 
other  beaker.  Add  ice  to  the  calorimeter,  a  very  little  at  a  time, 
stirring  constantly  with  the  stirrer  on  the  thermometer.  Watch 
closely  meanwhile  for  the  first  deposit  of  moisture  on  the  calorim- 
eter near  the  bottom ;  and  when  it  appears,  take  the  tempera- 
ture of  the  water.  It  is  the  highest  temperature  at  which 
moisture  is  deposited  that  is  to  be  found.  If  the  moisture 
gathers  quickly  and  abundantly,  the  water  is  too  cold.  If  this 
happens,  add  warmer  water  to  the  calorimeter,  wipe  the  outside 
dry,  and  repeat,  being  careful  to  cool  the  water  more  gradually. 
Avoid  breathing  on  the  calorimeter.  (Why?)  If  the  dew-point 
is  below  zero,  it  will  be  necessary  to  add  salt  with  the  ice.  If  in 
the  course  of  the  experiment  the  calorimeter  becomes  more  than 
half  full,  pour  out  part  of  the  contents. 

b.  Starting  with  a  thin  film  of  moisture  on  the  calorimeter,  stir 
the  water  constantly  till  the  moisture  disappears,  then  take  the 
temperature.  The  temperatures  at  which  the  dew  appears  and 
disappears  should  not  differ  by  more  than  i°.  Take  their  aver- 
age as  the  dew-point  of  the  air  in  the  laboratory  at  the  time  of 
the  experiment. 


PHENOMENA   OF   BOILING 


III 


EXERCISE   33.     PHENOMENA   OF   BOILING 

References.  —  Adams,  393-395;  Coleman,  261-262;  Car.  & 
C.,  337  ;  Ches.  G.  &  T.,  251-254  ;  Hoad.  Br.,  277  ;  Hoad.  EL, 
306;  Mumper,  128-129;  Mil.  &  G.,  278-280;  Went.  &  H.,  104. 

Apparatus.  —  Ther- 

mometer,     numbered 

for  identification  ;  ring 

stand,  ring  and  clamp  ; 

wire  gauze  ;  large  flask, 

and  stopper  to  fit,  with 

two     holes  ;     delivery 

tube    (Fig.    44)  ;    hy- 

drometer jar  ;  Bunsen 

burner  ;     closed  -tube 

pressure    gauge     con- 

taining   water    in    the 

closed  tube  above  the 

mercury  (Fig.  45). 
[To  make  the  pres- 

sure    gauge,     take     a 

piece  of  small  glass  tubing  about  a  foot  long  ;  seal  one 
end,  and  bend  about  3  in.  from  the  closed  end,  as  shown 
in  Figure  45,  making  the  bend  narrow  enough  to  pass 
through  the  neck  of  the  flask.  A  slight  bend  in  the 
open  arm  of  the  tube,  at  right  angles  to  the  two  arms,  as 
shown  in  the  figure,  will  keep  the  mercury  from  running 
out  when  the  tube  is  laid  on  the  table.  Pour  in  enough 
mercury  to  fill  the  short  arm  and  extend  just  past  the  bend. 
By  holding  the  tube  horizontal,  with  the  closed  end  below, 
and  inclining  it  first  in  one  direction  then  in  the  other, 
the  air  can  be  gradually  displaced  from  the  closed  end 
by  the  mercury.  Next  pour  in  water  to  a  depth  of 
about  half  an  inch,  and  work  a  little  of  it  into  the  closed 

FIG.  45.    arm  by  inclining  the  tube  with  the  closed  arm  above.] 


FlG- 


112  HEAT 

Experiment  62. —  To  observe  the  phenomena  preceding  and  ac- 
companying boiling;  and  to  find  the  temperature  of  the  boiling 
water  and  the  steam. 

Experimental  Work.  —  Fill  the  flask  about  half  full  of  fresh 
water  (not  water  that  has  been  boiled),  wipe  the  outside  dry, 
place  it  on  the  wire  gauze  on  the  stand,  and  apply  heat.  The 
flame  must  not  be  high  enough  to  burn  above  the  gauze.  While 
the  water  is  heating,  conduct  simultaneously  the  observations 
called  for  in  paragraphs  a,  b,  and  c. 

a.  Place  the  thermometer  in  the  flask,  letting  it  rest  on  the 
bottom,  and  occasionally  observe  the  temperature.     Observe  the 
water  while   heating,  and   note    the  first  formation  of  bubbles. 
These  are  bubbles  of  air  which  was  dissolved  in  the  water  and 
which  is  now  being  driven  off  by  the  heat.     Describe  their  size, 
abundance,  and  behavior ;  and  state  through  what  range  of  tem- 
perature  (approximately)   they  continue  to  be  given  off.      (The 

•  "  flat "  taste  of  boiled  water  is  due  to  the  fact  that  it  contains 
little  or  no  dissolved  air.) 

b.  Note  any  gathering  of  moisture  on  the  inside  of  the  flask 
and  on  the  thermometer.     Does  it  occur  before  the  water  boils  ? 
How  do  you  account  for  it? 

c.  Note  the  temperature  when  sounds  begin  to  come  from  the 
flask.    What  is  their  cause  ?    Is  the  water  boiling  when  the  sounds 
begin  ?     Watch  closely  for  the  first  formation  of  bubbles  larger 
than  the  air  bubbles  first  observed.     What  are  they?      Where  are 
they  formed  ?     What  becomes  of  them  ?     Note  the  temperature. 
Watch  closely  for  any  change  in  the  phenomena  as  the  tempera- 
ture approaches  100°. 

d.  Regulate  the  flame  so  that  the  water  boils  slowly,  and  record 
its   temperature.      Record   its   temperature   when   it    is    boiling 
rapidly. 

e.  Raise  the  thermometer  till  the  bulb  is  just  out  of  the  water. 
Take  the  temperature  as  accurately  as  possible  and  record  it  as 
the  temperature  of  the  steam. 


PHENOMENA   OF   BOILING  113 

Experiment  63.  —  To  find  the  vapor  pressure  of  steam  at  the 

boiling  point. 

Experimental  Work.  —  The  closed-tube  pressure  gauge  (Fig.  45) 
contains  water  in  the  closed  arm  above  the  mercury.  If  there  is 
a  bubble  at  the  top  of  the  closed  tube,  it  is  air,  and  mast  be 
removed.  Have  this  done  by  the  instructor.  Lower  the  gauge 
into  the  steam  above  the  boiling  water  in  the  flask,  and  note  the 
formation  of  water  vapor  in  the  closed  arm.  How  do  the  levels 
of  the  mercury  in  the  two  arms  compare?  What  does  this 
prove  concerning  the  relative  values  of  the  atmospheric  pressure 
and  the  pressure  of  the  water  vapor  in  the  closed  arm  ?  Observe 
the  effect  of  removing  the  gauge  from  the  flask.  Explain. 

Conclusions.  —  State  the  conclusions  to  be  drawn  from  the 
experiment. 

Experiment  64. —  To  observe  the  effect  of  increase  of  pressure 
upon  the  boiling  point ;  and  to  find  the  correction  for  the  boiling 
point  on  the  thermometer  used. 

Experimental  Work.  —  Remove  the  burner  from  under  the  flask 
while  you  are  making  the  following  adjustment.  Push  the  ther- 
mometer through  the  hole  in  the  stopper  till  the  bulb  is  but  little 
above  the  water  when  the  stopper  is  in  the  flask.  Be  careful ;  if 
you  have  difficulty,  call  for  assistance.  Press  the  stopper  firmly 
into  the  flask.  Connect  the  delivery  tube  as  shown  in  Figure  44, 
and  let  it  extend  to  the  bottom  of  the  hydrometer  jar,  which 
should  be  nearly  full  of  water.  Boil  the  water  in  the  flask,  and 
take  the  temperature  of  the  steam  while  it  is  escaping  into  the 
bottom  of  the  jar  of  water.  (The  noise  of  the  condensing  steam 
can  be  greatly  reduced  by  standing  the  jar  on  a  book.)  Gradually 
raise  the  delivery  tube  out  of  the  jar  while  observing  the  effect 
upon  the  temperature  of  the  steam.  Raise  and  lower  the  tube 
till  you  are  sure  of  the  effect.  Take  the  temperature  while  the 
steam  is  escaping  into  the  air.  Empty  the  flask  and  return  the 
thermometer  to  its  case. 

Read  the  barometer. 

COLEMAN'S  NEW  MANUAL — 8 


114 


HEAT 


Discussion.  —  i.  Discuss  the  experiment  as  an  illustration  of 
the  effect  of  pressure  on  the  temperature  at  which  water  boils. 

2.  At  a  pressure  of  one  atmosphere  (76  cm.)  the  true  value  of 
the  boiling  point  is  100°.     For  pressures  either  slightly  greater  or 
less  than  one  atmosphere,  the  temperature  of  steam  from  boiling 
water  varies  .37°  for  a  change  of  pressure  of  i  cm.     Compute  the 
true  value  of  the  temperature  of  steam  at  the  observed  barometric 
pressure. 

3.  What  is  the  error  of  the  boiling  point  on  this  thermometer? 

EXERCISE  34.     HEAT  OF  VAPORIZATION  OF  WATER 

References.  —  Adams,  396;  Coleman,  266-267;  Car.  &  C., 
342  ;  Ches.  G.  &  T.,  245,  255  ;  Hoad.  Br.,  285-286;  Hoad.  El., 
317-318;  Mumper,  133  ;  Mil.  &  G.,  275-277  ;  Went.  &  H.,  112. 

Experiment  65.  —  To  find  the  number  of  calories  given  out  by 
i  g.  of  steam  at  100°  in  condensing  to  water  at  100°. 

Apparatus.  —  Flask  or  other  steam-generating  apparatus,  with 
rubber  tube  and  condensation  trap  (Fig.  46)  or  side-neck  test 

tube  ;  Bunsen  burner  ;  calorim- 
eter ;  thermometer  and  stirrer ; 
platform  balance  and  weights; 
ice ;  mop  cloth. 

Experimental  Work.  —  Fill 
the  steam  generator  about  half 
full  of  water,  and  begin  heating 
it.  Connect  the  delivery  tube 
and  condensation  trap.  Sup- 
port the  delivery  tube  on  some 
object  so  that  the  escaping 
steam  will  not  damage  the  table. 

Weigh  the  calorimeter  to  .1  g. 

FIG'  46'  (It  is  especially  important  ir 

this  experiment  that  the  weighing  be  carefully  done.)  Fill 


HEAT   OF   VAPORIZATION   OF   WATER  1 15 

calorimeter  about  two  thirds  full  of  water  at  o°  to  5°.  Add  ice  to 
water  from  the  faucet  till  the  required  temperature  is  obtained. 
(If  ice  is  not  provided,  use  the  coldest  water  obtainable.) 
Weigh  the  calorimeter  and  water,  and  remove  at  once  from  the 
balance. 

Place  the  stirrer  on  the  thermometer,  and  as  soon  as  the  steam 
is  escaping  freely  from  the  delivery  tube,  stir  the  water  in  the 
calorimeter  and  take  the  temperature.  Wipe  off  any  dew  that  has 
gathered  on  the  calorimeter,  and  immediately  place  the  delivery 
tube  in  the  water  to  a  depth  of  an  inch  or  two.  The  calorimeter 
should  be  at  some  distance  from  the  burner  and  protected  from 
its  radiation  by  a  screen.  Stand  your  note  book  between  them 
for  this  purpose.  There  should  be  no  considerable  loss  of  steam 
on  account  of  poorly  adjusted  apparatus.  If  the  steam  is  delivered 
properly,  the  temperature  will  rise  rapidly.  Stir  the  water  con- 
stantly, keeping  the  hands  off  the  calorimeter.  The  condensation 
trap  must  not  overflow  and  admit  hot  water  into  the  calorimeter. 
To  empty  it,  remove  the  burner  from  under  the  boiler  and  lift  the 
delivery  tube  till  the  water  in  the  trap  runs  back  into  the  boiler. 

When  the  temperature  has  risen  to  about  40°,  turn  off  the  gas, 
remove  the  delivery  tube  from  the  calorimeter  immediately,  stir 
the  water  thoroughly,  and  take  the  temperature  as  quickly  as 
possible. 

Weigh  the  calorimeter  and  contents.  Leave  the  calorimeter 
empty  and  the  table  dry. 

Data  and  Computations.  —  The  temperatures  in  the  experiment 
are  so  chosen  that  the  heat  received  from  outside  bodies  while  the 
calorimeter  and  water  are  colder  than  the  air  is  as  nearly  as  possi- 
ble equal  to  the  heat  gained  after  they  have  become  warmer  than 
the  air.  Hence  the  heat  gained  by  the  water  and  calorimeter  is 
assumed  to  come  only  from  the  steam,  first  in  condensing  to  water 
at  100°,  second  in  cooling  to  the  final  temperature.  Let  v  denote 
the  heat  of  vaporization  of  water  (the  number  of  calories  given 
out  by  one  gram  of  steam  in  condensing  to  water  at  100°).  Write 


Il6  HEAT 

the  heat  equation,  and  solve  it  for  v.     Record  data  and  computa- 
tions as  follows  :  — 

Weight  of  calorimeter  =         g. 

Weight  of  calorimeter  and  water  g. 

Temperature  of  calorimeter  and  water  just  before  add- 
ing steam  =  ° 

Final  temperature  of  calorimeter  and  water  = 

Final  weight  of  calorimeter  and  water  (including  water 

from  steam)  =  g. 

COMPUTATIONS 

Weight  of  water  before  adding  steam  =        g. 

Weight  of  steam  added  =         g. 

Rise  of  temperature  of  calorimeter  and  water  = 

Heat  received  by  the  calorimeter  =         cal. 

Heat  received  by  the  water  =         cal. 

Heat  given  out  by  the  steam  in  condensing  to  water  at 

ioo°=  (  )  x  v  cal. 

Heat  given  out  by  water  from  condensed  steam  in  cool- 
ing to  final  temperature  cal 

Heat  equation  and  its  solution  :  — 

Computed  heat  of  vaporization  of  water,  v  cal. 

True  value  of  heat  of  vaporization  of  water  =  536  cal. 

Percentage  of  error  =          % 


EXERCISE  35.     THE  STEAM  ENGINE 
(INVENTIVE) 

References.  —  Adams,  362-368  ;  Coleman,  275-276 ;  Car.  &  C., 
.357;  Ches.  G.  &  T.,  257-260;  Hoad.  Br.,  289;  Hoad.  EL, 
321-322;  Mumper,  156;  Mil.  &  G.,  252-258;  Went.  &  H.,  230- 
233- 

Experiment  66.  —  To  study  the  mechanism  of  a  steam  engine. 

Apparatus.  —  Section  model  of  a  steam  engine  (Fig.  47). 


THE  STEAM   ENGINE 


117 


Suggestions.  —  Study  the  model  in  connection  with  the  text 
and  reference  books.  Describe  the  points  illustrated  by  the 
model,  referring  to  lettered  diagrams  of  its  various  parts.  A  model 
like  that  shown  in  the 
figure  is  provided  with 
the  reversing  gear  used 
on  locomotives.  The 
reversing  gear  is  oper- 
ated by  means  of  the 
lever.  Find  the  direc- 
tion in  which  the  driv- 
ing wheel  of  the  actual 
engine  represented  by 
the  model  would  turn 
when  the  lever  is  in 


FIG.  47. 


the  extreme  front  and  back  positions.  What  would  be  the  effect 
of  placing  the  lever  midway  between  these  positions  ?  Study  the 
effect  of  setting  the  lever  part  way  forward  and  part  way  back. 
In  discussing  the  reversing  gear,  refer  to  lettered  diagrams  of  it. 


VIII.   SOUND 

EXERCISE  36.     THE  TRANSMISSION    OF   SOUND 

References.  —  Adams,  208  ;  Coleman,  277-280,290;  Car.  & 
C.,  174-179,  198-199;  Ches.  G.  &  T.,  167-170;  Hoad.  Br., 
181-184;  Hoad.  EL,  195-198;  Mumper,  162-165;  Mil.  &  G., 
444-445  ;  Went-  &  H.,  333-334. 

Experiment  67. —  To  study  the  transmission  of  sound  through 
solids. 

Apparatus.  —  Meter  rod ;  large  tuning  fork ;  rubber  mallet  for 
striking  the  fork  ;  cord  four  or  five  feet  long. 

[For  a  rubber  mallet  bore  a  half-inch  hole  in  a  large  rubber 
stopper,  and  insert  a  stick  about  10  in.  long  for  a  handle ;  or  slip 
a  short  piece  of  large,  thick  rubber  tubing  on  the  end  of  a  stick.] 

Experimental  Work. — a.  To  set  a  tuning  fork  in  vibration, 
hold  it  by  the  stem  in  one  hand  and  strike  one  of  the  prongs  a 
sharp,  quick  blow  near  its  end,  in  the  direction  of  the  other  prong. 
(Touching  a  prong  of  a  sounding  fork  immediately  stops  it.) 
Hold  one  end  of  the  meter  rod  close  to  the  ear  while  your  com- 
panion holds  the  stem  of  the  vibrating  fork  against  the  other  end 
of  the  rod.  Note  the  loudness  of  the  sound.  Listen  to  the  sound 
of  the  fork  through  the  air  at  the  same  distance,  the  rod  being 
removed.  Compare  the  loudness  of  the  sound  transmitted  through 
the  rod  and  through  the  air. 

b.  Hold  an  end  of  the  rod  between  your  teeth  while  the  stem 
of  the  sounding  fork  is  held  against  the  other  end.  The  sound 
travels  through  the  rod,  the  teeth,  and  the  bones  of  the  head  to 
the  ear.  Describe  the  result.  Do  you  feel  the  vibrations? 

118 


THE  TRANSMISSION   OF   SOUND  Iig 

c.  Hold  the  stem  of  the  vibrating  fork  against  the  teeth  ;  against 
the  top  of  the  head.     State  the  result. 

d.  Tie  a  string  one  or  two  meters  long  to  the  stem  of  the  fork. 
Press  one  end  of  the  string  into  your  ear,  while  your  companion 
sets  the  fork  vibrating  and  holds  it  so  as  to  stretch  the  string  moder- 
ately  tight.     Try   the   effect   of  slackening  the  string ;  also  the 
effect  of  removing  it  from  the  ear  when  tightly  stretched.     What 
have  you  learned  about  the  transmission  of  sound  by  the  string? 

e.  Touch  the  stem  of  the  vibrating  fork  to  the  table  top.     The 
loud  sound  comes  from  the  table,  which  is  set  in  vibration  by  the 
fork.     Hold  an  end  of  the  meter  rod  against  the  side  of  the  table, 
and  the  vibrating  fork  against  the  other  end  of  the  rod.    State  and 
account  for  the  result. 

/.  Place  the  rubber  stopper  of  the  mallet  between  the  vibrating 
fork  and  the  table.  How  does  the  stopper  compare  with  the  rod 
in  its  power  to  transmit  sound?  To  what  is  the  difference  due? 

Experiment  68.  —  To  study  the  construction  and  use  of  an 
acoustic  telephone  line. 

Apparatus.  —  An  acoustic  telephone  line,  with  stations  at  oppo- 
site ends  of  the  laboratory  or  in  adjacent  rooms  j  tuning  fork ; 
mallet. 

[To  make  an  acoustic  telephone,  make  a  small  hole  in  the  mid- 
dle of  the  bottom  of  two  small  tin  cans  or  chalk  boxes,  fasten 
them  up  at  some  distance  apart,  and  stretch  a  cord  or  small  copper 
wire  rather  tightly  between  them,  fastening  the  ends  to  some  small 
object,  as  a  button,  on  the  inside  of  the  bottom  of  the  cans.  The 
cord  must  not  be  supported  by  fastening  it  rigidly  to  any  object. 
It  may  be  supported  at  any  point  by  a  short  cord,  and  may  be 
carried  round  a  corner  by  giving  it  three  or  four  such  supports  at 
the  corner,  making  each  bend  slight.  The  acoustic  telephones 
supplied  by  dealers  are  more  satisfactory.] 

Experimental  Work.  —  Listen  at  one  end  of  the  telephone  line, 
while  your  companion  places  the  stem  of  a  vibrating  fork  against 


120  SOUND 

the  telephone  at  the  other  end.     Try  speaking  to  each   other 
through  the  telephones. 

Note  the  construction  of  the  telephones  and  the  manner  in 
which  the  connecting  wire  (or  cord)  is  supported.  Describe  the 
various  details  observed,  and  explain  their  purpose. 

Experiment  69. —  To  find  whether  water  transmits  sound. 

Apparatus.  —  Battery  jar  of  water ;  large  tuning  fork ;  large 
cork  or  small  block  of  wood  with  hole  to  fit  the  stem  of  the  fork ; 
rubber  mallet. 

Experimental  Work.  —  Place  a  jar  of  water  on  the  table.  In- 
sert the  stem  of  the  fork  into  the  hole  in  the  cork  (or  block). 
Set  the  fork  in  vibration  and  hold  it  with  the  cork  immersed  in 
the  water,  but  not  touching  the  glass.  Raise  the  cork  out  of  the 
water  and  again  immerse  it,  repeating  the  process  a  number  of 
times,  and  note  the  effect  on  the  loudness  of  the  sound.  State 
the  result. 

With  the  fork  sounding  and  its  stem  in  the  water,  try  the  effect 
of  lifting  the  jar  from  the  table  and  again  replacing  it.  Does  the 
sound  come  principally  from  the  jar  of  water  or  from  the  table 
when  the  jar  stands  on  the  table? 

How  does  the  experiment  answer  the  question  whether  water 
transmits  sound? 

Experiment  70.  —  To  study  the  transmission  of  sound  through 
a  speaking  tube. 

Apparatus.  —  A  tin  or  large  glass  tube  6  ft.  to  10  ft.  long;  roll 
of  cotton  or  soft  cloth  ;  watch. 

Experimental  Work.  —  Lay  a  watch  on  a  roll  of  cotton  or  soft 
cloth  (to  prevent  the  transmission  of  the  sound  through  the  table) 
at  one  end  of  the  tube,  and  listen  at  the  other  end  to  the  sound 
of  the  ticking.  About  how  near  to  the  watch  must  you  hold  the 
-ear  to  hear  it  as  distinctly  directly  through  the  air  as  through  the 
tube  ? 

Explain  the  effect  of  the  tube. 


RIPPLES.     REFLECTION   OF  SOUND  121 

EXERCISES   37.      RIPPLES.      REFLECTION    OF   SOUND 

References.  —  Adams,  195-196,  213;  Coleman,  281-283,  293  > 
Car.  &  C.,  164-165,  167,  169-172,  184-186;  Ches.  G.  &T.,  170- 
173,  181;  Hoad.  Br.,  185-188,  193-195;  Hoad.  EL,  200-203, 
209-211;  Mumper,  157-160,  165,  167;  Mil.  &  G.,  448-455, 
459-460;  Went.  &  H.,  334-338.  340-34L 

Experiment  71.  —  To  study  the  origin,  transmission,  and  reflec- 
tion of  ripples. 

Apparatus.  —  Ripple  trough,  strip  of  tin  about  2  in.  wide  and 
about  the  width  of  the  trough,  bent  into  an  arc  of  about  70° ;  thin 
board  about  3  in.  wide  and  a  trifle  shorter  than  the  width  of  the 
trough. 

[The  ripple  trough  is  a  shallow  box  with  a  glass  bottom.  For 
the  sides  use  1.5  x  2.5  in.  wood  or  larger,  and  for  the  bottom 
a  window  pane  not  smaller  than  20X24  in.,  —  larger,  up  to 
24  x  30  in.,  is  preferable.  Plate  glass  gives  a  uniform  depth  of 
water,  which  is  very  desirable.  The  wooden  sides  should  be 
given  two  or  three  coats  of  boiled  oil  or  a  coat  of  hot  paraffine 
to  prevent  absorption  of  water.  An  inch  hole  should  be  bored 
in  one  end  and  closed  with  a  cork,  for  convenience  in  emptying 
the  trough.] 

Experimental  Work.  —  a.  Origin  and  propagation  of  waves.  — 
Spread  a  large  sheet  of  white  or  very  light  colored  paper  on 
a  table  near  a  window  where 'the  light  is  strong,  and  place  the 
trough  on  the  paper.  This  arrangement  makes  the  ripples 
distinctly  visible.  Fill  the  trough  with,  water  to  a  depth  of  about 
i  cm.  Start  a  wave  at  the  center  of  the  trough  by  dipping  the 
finger  into  the  trough  and  quickly  removing  it.  Observe  the  shape 
of  the  wave  and  the  direction  or  directions  in  which  it  travels. 
Repeat  till  sure  of  the  results.  Describe  what  is  observed. 

b.  Start  a  series  or  train  of  waves  by  tapping  rapidly  with 
the  finger  at  the  center  of  the  trough.  Describe  the  appearance 
of  the  train  of  waves  and  their  behavior. 


122 


SOUND 


FIG.  48. 


c.   Place  the  board  on  edge  in  the  trough  in  the  position  shown 
at  ab  (Fig.  48).    With  a  slight  forward  and  backward  motion  of 

the  board,  start  a  wave  down  the  trough. 

Describe  the  shape  and  behavior  of  the 

wave,  and  compare   it  with   the  wave 

set  up  by  the  finger. 

d.    Start  a  train  of  waves  by  means 

of  the  board.     Compare  with  the  train 

of  waves  set  up  by  rapid  tapping  with 

the  finger. 

Reflection    of    Waves.  —  e.    Start    a 
straight  wave  with  the  board,  as  in  c,  and  observe  what  happens 
when  the  wave  reaches  the  farther  end  of  the  trough.     Start  a 
train  of  three  or  four  waves,  and  observe 
whether  they   are   all   reflected.     Can 
two  sets  of  waves  travel  over  the  same 
surface   in  opposite  directions  and   at 
the  same  time? 

f.  Start  a  train  of  waves  with  the 
board  at  an  angle  with  the  side  of  the 
trough,  as  in  the  position  ab  (Fig.  49). 
Draw  a  diagram  showing  the  course  of 
these  waves  before  and  after  reflection, 
waves  by  a  number  of  parallel  lines.) 


FIG.  50. 


FIG.  49. 

(Represent  a  train  of 
Describe  the  reflection 
of  an  oblique  wave  and  its  change  of 
direction*. 

g.  Start  a  circular  wave  at  the  center 
of  the  trough  by  a  tap  with  the  finger, 
and  observe  its  reflection  by  the  sides 
of  the  tank.  Start  a  train  of  waves, 
and  observe.  Describe,  with  a  diagram 
to  illustrate. 

h.    Place  the  curved  strip  of  tin   as 


shown  at  cd  (Fig.   50),    and    observe  the  reflection  of  a  single 
straight  wave  and  also  a  train  of  straight  waves  from  its  concave 


RIPPLES.     REFLECTION   OF  SOUND  123 

side.     Describe  the  shape  and  behavior  of  the  reflected  waves,  and 
draw  a  diagram  to  illustrate. 

Experiment  72.  —  To  study  the  reflection  of  sound  from  concave 
surfaces. 

Apparatus.  —  Two  large  concave  reflectors;  large  funnel  with 
rubber  tube  attached,  for  use  as  an  ear  trumpet ;  watch. 

[This  experiment  can  be  performed  only  in  a  very  quiet  room. 
It  should  be  set  up  in  a  room  by  itself,  if  possible.] 

Experimental  Work.  —  a.  Stand  one  of  the  reflectors  (A,  Fig. 
51)  at  one  end  of  the  table,  and  turn  it  so  as  to  face  toward  the 
other  reflector  B,  placed  at  a  distance  of  3  or  4  m.  B  is  set 


FIG.  51. 

obliquely,  as  shown  in  the  figure.  Hang  a  watch  in  front  of 
the  center  of  reflector  A  at  a  distance  from  it  equal  to  half  the 
radius  of  its  spherical  surface.  This  point  F  is  called  the 
principal  focus  of  the  reflector. 

Hold  the  ear  at  E,  being  careful  to  cover  as  little  of  the  reflector 
with  the  head  as  possible,  so  as  not  to  intercept  the  sound  waves 
as  they  travel  from  A  to  B.  Move  the  head  slightly  in  different 
directions  to  find  the  position  where  the  sound  is  loudest.  When 
the  ear  is  properly  placed,  the  watch  should  be  heard  distinctly. 

b.  Instead  of  placing  the  ear  at  E,  the  reflector  B  may  be  turned 
so  as  to  face  squarely  toward  A,  and  the  ear  trumpet  used  to  con- 
vey the  sound  to  the  ear.     Place  the  funnel  at  the  focus  of  B,  and 
facing  toward  it,  and  the  end  of  the  tube  in  the  ear.    Try  both  ways. 

c.  With    the    ear   at  E  or  with  the  ear  trumpet   in    position, 
observe  the  effect  of  turning  A  about  a  vertical  axis  toward  one 
side,  then  toward  the  other. 


124 


SOUND 


EXERCISE  38.     VIBRATION  NUMBER  OF  A  FORK 

References.  —  Adams,  231-239  ;  Coleman,  294-296  ;  Car.  &  C., 
204-205  ;  Ches.  G.  &  T.,  185-186  ;  Hoad.  Br.,  205-207  ;  Hoad. 
EL,  201,  222  ;  Mumper,  172  ;  Mil.  £  G.,  456-457 ;  Went.  &  H., 
344- 

Experiment  73.  —  To  find  the  number  of  vibrations  per  second 
of  a  tuning  fork. 


FIG.  52. 


Apparatus.  —  Vibrograph  with  tuning  fork,  as  shown  in  Figure 
52  ;  rubber  mallet;  watch  or  small  clock  with  second-hand;  fluid 
paste  of  whiting  (or  chalk  dust)  and  alcohol ;  small  paint  brush. 

[The  pendulum  of  the  vibrograph  should  make  not  less  than  two 
double  vibrations  per  second,  and  must  have  a  heavy  bob  in  order 
that  the  friction  of  the  stylus  may  not  affect  its  rate  or  stop  it  too 
quickly.  The  fork  must  be  large  and  of  low  pitch,  preferably  not 
above  128,  and  capable  of  vibrating  with  a  large  amplitude  for 
several  seconds.  Dealers  supply  forks  especially  designed  for 
this  purpose.  The  glass  plate  should  be  a  foot  or  more  in  length, 
so  as  to  accommodate  at  least  two  double  vibrations  of  the  pendu- 


VIBRATION    NUMBER  OF  A   FORK  125 

him.  The  experiment  is  intolerably  dirty  in  the  hands  of  most 
pupils,  if  smoked  glass  is  used.  If  smoked  glass  is  preferred,  it 
is  recommended  that  the  teacher  smoke  the  plates  and  take  the 
traces  for  the  class.] 

Method.  —  A  stylus  of  fine  wire  or  bristle  is  attached  at  the 
lower  end  of  the  pendulum,  and  another  at  the  end  of  one  of  the 
prongs  of  the  fork.  These  styluses  lightly  touch  a  plate  of  glass 
placed  under  them  on  the  board.  The  glass  is  covered  on  its 
upper  side  with  a  thin  coating  of  whiting  and  alcohol  (or  is 
smoked).  With  the  fork  and  the  pendulum  vibrating,  the  glass  is 
drawn  quickly  along  the  board  to  the  right,  and  each  stylus  traces 
a  wavy  line  on  the  glass,  as  shown  in  Figure  53,  the  line  traced  by 
the  pendulum  crossing  and  recrossing  at  regular  intervals  the  one 


made  by  the  fork.  The  time  interval  from  A  to  C  in  the  figure 
is  the  time  of  a  double  vibration  of  the  pendulum,  which  is  com- 
puted from  the  number  of  double  vibrations  which  the  pendulum 
makes  in  one  minute.  The  number  of  vibrations  made  by  the 
fork  during  one  or  more  double  vibrations  of  the  pendulum  is 
found  from  the  trace  on  the  glass.  Having  thus  the  number  of 
vibrations  of  the  fork  in  a  known  interval  of  time,  the  number  of 
vibrations  per  second  is  easily  computed. 

Experimental  Work.  —  Paint  one  side  of  the  glass  plate  uniformly 
with  the  whiting  and  alcohol  paste,  and  lay  the  plate  aside  to  dry. 

Count  the  number  of  vibrations  that  the  pendulum  makes  in 
60  sec.,  and  compute  the  time  of  one  double  vibration. 

After  the  glass  is  dried,  place  it  in  position  with  its  right  end 
under  the  styluses,  being  careful  not  to  bend  them.  Adjust  the 


126  SOUND 

fork  and  the  pendulum  so  that  the  styluses  touch  the  glass  lightly, 
within  2  or  3  mm.  of  each  other  at  points  which  are  in  a  line 
parallel  to  the  sides  of  the  base.  Set  the  pendulum  swinging 
through  an  arc  of  about  3  cm.,  strike  the  fork  a  vigorous  blow  to 
give  it  a  large  amplitude,  and  immediately  draw  the  glass  with  a 
quick,  steady  motion  to  the  right.  Repeat,  if  necessary,  till  you 
have  obtained  a  good  trace  of  the  fork  covering  not  less  than  two 
double  vibrations  of  the  pendulum  (from  A  to  E  in  the  figure), 
if  this  seems  to  be  possible  with  the  apparatus  provided. 

Count  the  double  vibrations  of  the  fork  (estimating  tenths)  for 
the  greatest  number  of  whole  double  vibrations  of  the  pendulum 
recorded  on  the  glass  (A  to  C,  A  to  E,  or  A  to  G  in  the  figure). 
Only  whole  double  vibrations  of  the  pendulum  are  considered, 
since,  if  the  traces  of  the  fork  and  the  pendulum  do  not  lie  on 
exactly  the  same  axis,  adjacent  spaces  (as  BC  and  CD)  will  not 
be  exactly  equal,  one  representing  more  and  the  other  less  than  a 
single  vibration  of  the  pendulum. 

Data  and  Computations.  —  Record  as  follows:  — 

No.  of  double  vibrations  of  pendulum  in  60  sec.  = 

Time  of  one  double  vibration  of  pendulum  = 

No.  of  vibrations  of  fork  to double  vibrations  of 

pendulum  (counted)  = 

No.  of  vibrations  of  fork  to  one  double  vibration  of  pen- 
dulum (computed)  = 
No.  of  vibrations  of  fork  per  second  = 

EXERCISE   39.     INTERFERENCE   AND   BEATS 

References.  —  Adams,  201,  220-223;  Coleman,  298-299;  Car. 
&  C.,  201-203;  Ches.  G.  &  T.,  195,  200;  Hoad.  Br.,  196-197, 
204;  Hoad.  El.,  212,  219;  Mumper,  171,  177;  Mil.  &  G.,  468; 
Went.  &  H.,  353-354- 

Experiment  74.  —  To  study  the  interference  of  sound  waves 
about  a  tuning  fork. 


INTERFERENCE  AND   BEATS  127 

Apparatus  (for  Experiments  74  and  75).  —  Two  tuning  forks 
nominally  of  the  same  pitch,  but  giving  from  one  to  three  beats 
per  second ;  cylinder  about  10  cm.  in  length  and  2  cm.  in  diam- 
eter, consisting  of  an  open  roll  of  writing  paper  fastened  with 
paste  or  a  rubber  band ;  rubber  mallet ;  soft  wax. 

[To  make  the  soft  wax,  melt  together  about  nine  parts,  by 
weight,  of  beeswax  and  one  part  of  Venice  turpentine.  Pour  the 
melted  wax  into  slender  cylindrical  paper  molds.  The  paper 
may  be  removed  as  the  wax  is  used.] 

Experimental  Work.  —  a.  Hold  a  vibrating  fork  in  a  vertical 
position  near  the  ear,  and  rotate  it  slowly.  Have  your  companion 
tell  you  the  position  of  the  plane  of  the  prongs  (whether  parallel 
with  the  side  of  the  face,  perpendicular  to  it,  or  at  a  greater  or 
less  angle)  when  the  sound  is  loudest  and  when  it  is  faintest  to 
you.  Describe  the  variations  in  the  intensity  of  the  sound,  and 
the  corresponding  positions  of  the  fork,  during  one  rotation. 
Note  whether  there  are  positions  in  which  the  sound  is  inaudible. 

b.  With  the  vibrating  fork  held  to  the  ear  in  the  position  in 
which  the  sound  is  faintest,  have  your  companion  cover  one  of  the 
prongs  with  the  paper  cylinder,  being  careful  not  to  touch  the 
fork  with  it.  Repeat  till  you  are  sure  of  the  effect.  State  it. 

Discussion.  —  State  briefly  the  cause  of  the  phenomena 
observed  in  these  experiments.  The  full  discussion  may  be  left 
for  the  recitation. 

Experiment  75. —  To  study  beats  by  means  of  two  tuning  forks 
of  very  nearly  the  same  pitch. 

Experimental  Work.  —  a.  Sound  both  forks  and  hold  them 
facing  each  other,  about  2  cm.  apart  and  close  to  the  ear,  with  the 
planes  of  the  prongs  perpendicular  to  the  side  of  the  face.  Note 
the  frequency  of  the  beats.  Sound  the  forks  and  touch  their 
stems  to  the  table.  Are  beats  produced? 

b.  Stick  a  piece  of  soft  wax  about  the  size  of  a  pea  to  a  prong 
of  one  of  the  forks,  near  the  end,  and  note  the  effect  on  the  fre- 


128 


SOUND 


quency  of  the  beats.  If  the  effect  is  too  small  to  be  noticed, 
use  more  wax.  It  is  better  to  stick  some  wax  on  both  prongs 
than  a  large  quantity  on  one.  The  effect  of  the  wax  on  the  fre- 
quency of  the  beats  will  depend  upon  whether  it  has  been  put  on 
the  fork  of  the  lower  or  the  higher  pitch.  Prove  this  by  remov- 
ing the  wax  and  putting  it  on  the  other  fork.  Does  loading  a 
fork  raise  or  lower  its  pitch  ?  Why  ? 

c.  Tune  the  forks  accurately  to  the  same  pitch  by  loading  the 
right  one  till  the  beats  cease.  Do  the 
beats  become  more  or  less  frequent  as 
the  forks  approach  unison? 

Experiment  76.  —  To  study  a  mechan- 
ical illustration  of  beats. 

Apparatus.  —  As  shown  in  Figure  54. 

\_BC  is  a  light,  thin  board  about  20  cm. 
long,  having  a  light  pointer  about  50  cm. 
long  fastened  to  one  end.  The  lower  end 
of  the  pointer  carries  a  small  white  card. 
The  board  is  free  to  swing  from  a  fixed 
support  E,  and  carries  two  pendulums, 
one  80  to  100  cm.  in  length,  the  other 
about  f  as  long.  The  bobs  of  the  pendu- 
lums are  of  equal  mass,  between  50  and 
200  g.  This  experiment  is  due  to  Pro- 
fessor Will  C.  Baker,  of  Queen's  University,  Kingston,  Ont] 

Experimental  Work.  —  Start  the  pendulums  together,  giving  the 
longer  one  an  amplitude  of  about  15°  and  the  shorter  an  ampli- 
tude a  few  degrees  greater.  Carefully  observe  :  (i)  the  gradual 
and  regular  alternation  of  the  pendulums  between  vibration 
together  (in  the  same  phase)  and  in  opposition  (in  opposite 
phase)  ;  (2)  the  behavior  of  the  pointer;  (3)  the  correspond- 
ence between  the  behavior  of  the  pendulums  and  the  behavior  of 
the  pointer. 


FIG.  54. 


THE  LAW  OF   LENGTHS  129 

Describe  the  observed  phenomena,  and  show  how  the  behavioi 
of  the  pointer  results  from  the  behavior  of  the  pendulums. 

Class  Discussion. — This  experiment  affords  visible  illustration 
of  the  mechanical  relations  involved  in  the  production  of  beats  in 
sound.  Study  the  experiment  from  this  point  of  view,  and  discuss 
it  in  the  recitation. 

EXERCISE   40.     THE   LAW   OF   LENGTHS1 

References.  —  Adams,  245;  Coleman,  305-307;  Car.  &  C., 
210-211  ;  Ches.  G.  &  T.,  199;  Hoad.  Br.,  220-222;  Hoad.  EL, 
233-234;  Mumper,  181 ;  Mil.  &  G.,  475  ;  Went.  &  H.,  347. 

Experiment  77.  To  find  the  relation  between  the  length  of  a  vi- 
brating string  and  its  pitch,  the  tension  remaining  constant, 

Apparatus.  —  Sonometer  (Fig.  55);  rubber  mallet;  three  or 
more  forks,  including  c1  (256  vibrations)  and  c"  (512);  meter  rod. 


55. 

Experimental  Work.  —  Adjust  the  bridge  of  the  sonometer  so 
that  the  vibrating  segment  of  the  wire  is  between  60  and  70  cm. 
long.  Vary  the  tension  till  the  wire  is  brought  nearly  into  unison 
with  the  c1  fork,  then  complete  the  adjustment  to  unison  by  vary- 
ing the  position  of  the  bridge.  In  doing  this,  the  vibrating  fork 
may  be  held  close  to  the  ear  (if  the  pupil  is  working  alone) 
or  touched  to  the  sonometer  or  to  the  top  of  the  table.  The  wire  • 
gives  a  better  sound  and  one  easier  to  compare  with  the  fork  if  it 

1  The  only  law  of  vibrating  strings  requiring  quantitative  treatment  in  ele- 
mentary physics  is  the  law  of  lengths.  This  law  underlies  the  discussion  of 
the  fundamental  tone,  overtones,  and  quality,  both  of  strings  and  vibrating  air 
columns,  and  may  therefore  be  conceded  a  place  in  the  laboratory  course, 
although  the  other  laws  receive  only  qualitative  illustration  in  the  classroom. 
COLEMAN'S  NEW  MANUAL — 9 


130 


SOUND 


is  plucked  near  the  middle  with  the  end  of  the  finger  (not  the 
nail).  When  the  wire  and  the  fork  are  nearly  in  unison,  note  the 
beats  and  tune  till  they  disappear.  Measure  the  length  of  the  vi- 
brating segment  of  the  wire  when  unison  is  exact.  The  tension 
must  now  remain  unchanged  throughout  the  exercise.  Displace 
the  bridge  and  make  a  second  trial.  Make  further  trials  if  the 
disagreement  exceeds  3  mm. 

Repeat  the  above  work  with  each  of  the  forks  provided,  tuning 
only  by  varying  the  length  of  the  wire. 

Data  and  Computations.  —  Tabulate  measurements  and  compu- 
tations as  indicated  below.  By  length  ratio  for  any  tone  is  meant 
the  ratio  of  the  length  of  the  wire  for  that  tone  to  the  length  of 
the  wire  for  c* .  Compute  the  length  ratio  in  each  case,  carrying 
to  three  decimal  places.  Find  the  true  values  of  the  length  ratios 
from  the  law  of  lengths  and  the  known  vibration  ratios  of  the  forks 
used.  For  example,  if  the  fork  is  g',  the  vibration  ratio  is  f,  and, 
by  the  law  of  lengths,  the  length  ratio  is  the  reciprocal  of  this,  or  f . 


LENGTH  OF  WIRE 

LENGTH  RATIO 

TONE 

MEAN 
LENGTH 

ERROR 

PERCENTAGE 
OF  ERROR 

ist  Trial 

2d  Trial 

By  Exp. 

True 

c> 

e> 

cm. 

cm. 

cm. 



.800 





jf 

cm. 

cm. 

cm. 



.667 





etc. 

cm. 

cm. 

—  cm. 









EXERCISE   41.     SYMPATHETIC   AND    FORCED 
VIBRATIONS 

References.  —  Adams,  214-215  ;  Coleman,  310-315  ;  Car.  &  C., 
189-193;  Ches.  G.  &  T.,  194-196;  Hoad.  Br.,  198,  202-203, 
205;  Hoad.  El.,  213-215,217-218;  Mumper,  168-169;  Mil.  &  G., 
456,  463,  467  ;  Went.  &  H.,  351-352. 


SYMPATHETIC  AND   FORCED   VIBRATIONS  131 

Experiment  78.  —  To  study  the  sympathetic  vibration  of  tuning 
forks  and  resonators. 

Apparatus. —  Two  tuning  forks  of  exactly  the  same  pitch 
(shown  by  the  absence  of  beats  when  sounded  together)  ; 
rubber  mallet;  soft  wax;  set  of  three  or  four  tin  tubes,  or 
short  pieces  of  large  glass  tubing,  of  different  length  and 
diameter. 

[Forks  giving  a  few  beats  per  second  can  be  permanently 
tuned  to  unison  by  filing  a  little  off  the  inside  of  the  prongs  at  the 
base  of  the  higher  fork  or  the  free  ends  of  the  lower  one.  It  will 
be  more  interesting  if  the  tubes  are  of  such  sizes  as  to  sound  a 
major  chord.  A  set  of  four  tin  tubes  haying  lengths  of  10,  8,  6.7, 
and  5  in.,  and  diameters  in  proportion  to  the  lengths,  will  do 
this.] 

Experimental  Work.  —  a.  Place  the  stem  of  a  sounding  fork 
against  the  teeth.  What  evidence  do  you  find  that  the  stem 
vibrates  as  well  as  the  prongs?  Is  the  vibration  of  the  stem 
longitudinal  or  transverse  ? 

b.  With  one  fork  sounding  and  the  other  silent,  place  the  ends 
of  their  stems  together ;  and  after  they  have  been  in  contact  one 
or  two  seconds,  hold  the  fork  that  was  silent  close  to  the  ear.     It 
will   be  found  to  be  vibrating   audibly.      How  was  its  vibration 
produced  ? 

c.  Sound  one  of  the  forks  and  hold  it  and  the  other  fork  close 
together,  facing  each  other,  but  not  touching.     After  one  or  two 
seconds,  hold  the  fork  that  was  silent  close  to  the  ear.     It  should 
be  sounding ;  if  it  is  not,  repeat.     Explain. 

d.  Stick  a  bit  of  wax  about  twice  the  size  of  a  pea  near  the  end 
of  a  prong  of  one  of  the  forks.     This  will  slightly  change  the  rate 
of  vibration  of  the  fork  (see  Experiment  75).     Now  repeat  the 
experiments  of  paragraphs  b  and  <r,  sounding  either  of  the  forks, 
and  observe  whether  the  silent  fork  is  made  to  vibrate.     State  and 
account  for  the  result. 

e.  Blow  across  the  ends  of  the  tubes  in  succession.     Note  that 


132  SOUND 

each  tube  gives  forth  a  sound  of  definite  pitch.  Hold  the  tubes 
close  to  the  ears,  using  both  ears  at  once,  and  note  the  faint 
sounds,  like  the  roar  of  a  sea  shell,  coming  from  them.  Note 
whether  the  loudness  of  the  sounds  coming  from  the  tubes  is 
affected  by  scraping  the  foot  on  the  floor  while  the  tubes  are  at 
the  ears.  Note  the  pitch  of  these  sounds.  Is  it  the  same  in 
each  case  as  that  produced  by  blowing  across  the  end  cf  the 
tube? 

The  continuous  sounds  from  the  tubes  are  due  to  the  various 
noises  in  the  room.  Consult  texts  for  the  explanation. 

Experiment  79. —  To  study  the  sympathetic  and  forced  vibra- 
tion of  a  sonometer  wire. 

Apparatus.  —  Sonometer  (Fig.  55)  with  two  wires  of  the  same 
size,  and  without  a  bridge. 

Experimental  Work.  —  a.  Tighten  one  of  the  sonometer  wires 
till  it  sounds  a  note  of  medium  pitch,  and  tune  the  other  wire  to 
perfect  unison  with  it.  When  the  wires  are  nearly  in  unison, 
listen  for  a  periodic  pulsation  of  the  sound  (beats)  when  both 
wires  are  plucked.  Tune  till  the  beats  cease.  Now  sound  one  of 
the  wires,  and  the  other  will  immediately  begin  to  vibrate  visibly. 
Stop  the  first  wire,  and  the  sound  will  be  continued  with  consider- 
able intensity  by  the  other.  Is  this  a  case  of  sympathetic  or  forced 
vibration?  How  is  it  produced? 

b.  With  the  wires  of  the  sonometer  so  nearly  in  unison  that 
they  give  less  than  one  beat  per  second  when  sounded  together, 
sound  only  one  of  them  and  observe  the  behavior  of  the  other. 
It  should  vibrate  visibly  for  brief  intervals,  which  alternate  with 
intervals  of  rest.  Observe  that,  as  the  difference  in  pitch 
is  increased,  these  alternations  of  rest  and  vibration  become 
more  rapid,  and  the  maximum  amplitude  of  vibration  becomes 
less,  until  presently  the  silent  wire  ceases  to  respond  at  all  to 
the  vibrations  of  the  other.  Account  for  this  behavior  of  the 
wire. 


WAVE   LENGTH   BY   RESONANCE  133 

EXERCISE   42.     WAVE    LENGTH   BY   RESONANCE 

References.  —  Adams,  216-219  ;  Coleman,  313  ;  Car.  &  C.,  193; 
Ches.  G.  &  T.,  194-197;  Hoad.  Br.,  198-201  ;  Hoad.  EL,  216; 
Mil.  &  G.,  463-466  ;  Went.  &  H.,  349. 

Experiment  80.  —  To  find,  by  means  of  a  resonance  tube,  the 
length  of  the  sound  waves  set  up  by  a  tuning  fork  of  known  vibra- 
tion rate ;  and  to  compute  the  velocity  of  sound  in  air  frcm  these 
quantities. 

Apparatus.  —  Some  form  of  resonance  tube  having  an  adjustable 
length  (Figs.  56,  57,  and  58)  ;  tuning  fork;  rubber  mallet;  rub- 
ber band;  meter  rod;  access  to  a  thermometer. 


"FIG.  56. 

[For  second  resonance,  the  tube  must  be  at  least  105  cm.  long 
with  a  f1  fork  (256),  85  cm.  long  with  an  <?'  fork,  75  cm.  long  with 
a,g-'  fork,  and  55  cm.  long  with  a  c"  fork  (512).] 

Formula.  —  As  explained  in  the  text-books,  the  length  of  an  air 
column  giving  maximum  resonance,  in  a  tube  closed  at  one  end, 
is  \  of  the  wave  length  of  the  sound  for  first  resonance,  and  f  of 
the  wave  length  for  second  resonance.  The  vibrating  air  column, 
however,  extends  beyond  the  open  end  of  the  tube  a  distance 
approximately  equal  to  .3  of  the  inside  diameter  of  the  tube.  Let 
L  denote  the  wave  length,  ^  the  length  of  the  tube  for  first  reso- 
nance, and  /2  for  second  resonance,  and  d  its  inside  diameter; 
then  the  algebraic  statement  of  these  relations  is  ^-f  .$d=\L, 
and  /2  +  .3  d=  f  L  ;  from  which 

L  =  4  (/!  4-  .3  </),  for  first  resonance, 
L  =  2  (/2  —  /T),  for  second  resonance. 

It  should  be  noted  that  the  formula  for  second  resonance  does 


134 


SOUND 


not  involve  the  "correction  for  the  diameter,"  the  increase  of 
length  for  second  resonance  being  exactly  half  a  wave  length. 


Method.  —  The  vibrating  fork  is  held  within 
i  or  2  cm.  of  the  end  of  the  tube,  with  the 
plane  of  the  prongs  either  parallel  or  perpen- 
dicular to  the  axis  of  the  tube.  There  will  be 
almost  no  response  from  the  tube  unless  the 
length  of  the  air  column  is  nearly  that  neces- 
sary for  maximum  resonance,  the  length  of  the 
column  being  determined  by  the  position  of 
the  piston  (which  is  of  water  with  the  apparatus 
shown  in  Figures  57  and  58).  As  the  piston 
nears  the  correct  position,  the  sound  rapidly 
becomes  louder.  When  this  position  is  ap- 
proximately located,  the  piston  should  be 
moved  quickly  but  steadily  (not  with  sudden 
jerks)  back  and'  forth  past  it  several  times, 
through  a  gradually  diminishing  distance,  the 
experimenter  being  guided  by  the  regular 
swelling  and  dying  away  of  the  sound.  Mean- 
while the  rubber  band,  which  is  used  to  mark 


FIG.  57. 


the  correct  position,  is  gradually  shifted 
into  place.  The  adjustment  is  difficult 
and  requires  care. 

In  using  the  apparatus  shown  in  Figure 
5  7,  water  is  poured  in  till  it  stands  within 
25  or  30  cm.  of  the  top  of  the  tube  when 
the  funnel  is  about  half  full.  The  height  of 
the  water  in  the  tube  is  adjusted  by  raising 
and  lowering  the  funnel,  which  is  undamped 
and  held  in  the  hand.  With  the  apparatus 
shown  in  Figure  58,  the  length  of  the  air 
column  is  adjusted  by  raising  and  lowering 
the  tube  in  the  jar  of  water. 


;.  58. 


WAVE  LENGTH  BY  RESONANCE          135 

Experimental  Work.  —  Two  pupils  will  work  together,  one  man- 
aging the  fork  and  the  other  the  piston.  The  vibrating  fork  must 
not  be  permitted  to  touch  the  tube,  as  the  tube  may  be  broken. 
Find  the  length  of  the  tube  for  first  resonance.  Make  a  second 
trial,  after  moving  the  rubber  band  and  piston  out  of  position.  If 
the  two  results  do  not  differ  by  more  than  3  mm.,  take  their  aver- 
age as  the  value  of  4  If  the  difference  is  more  than  this,  repeat. 

Find  the  length  of  the  tube  for  second  resonance,  making  two 
or  more  trials  as  before,  and  call  their  average  /2.  (If  the  appa- 
ratus of  Figure  5  7  is  used,  it  may  be  necessary  to  pour  out  part  of 
the  water.  With  the  apparatus  of  Figure  58,  the  tube  is  too  short 
for  second  resonance  ;  in  which  case  determine  the  length  for  first 
resonance  with  a  fork  of  different  pitch.) 

Measure  the  inside  diameter  of  the  tube  d\  record  the  vibra- 
tion number  of  the  fork  n,  and  the  temperature  of  the  laboratory  /. 

Data  and  Computations.  —  Record  as  follows  :  — 

Length  of  tube  for  first  resonance        =  cm. 

Ditto,  second  trial                              =  cm. 

Ditto,  average  value,  JL                      =  cm. 

Length  of  tube  for  second  resonance  =  cm. 

Ditto,  second  trial                              =  cm. 

Ditto,  average  value,  /2                      =  cm. 

Diameter  of  the  tube  (inside)  d           =  cm. 
Vibration  number  of  the  fork  n           = 

Temperature  of  the  room  /                  =  °  C. 

Length  of  wave  L  =  4(4  -f  .3  (?)           =  cm. 

Length  of  wave  L  =  2(/2  —  /j)               =  cm. 

Discussion.  —  i .  From  the  known  vibration  number  of  the  fork 
and  the  value  of  L  given  by  the  experiment,  compute  the  velocity 
of  sound  in  air  at  the  temperature  of  the  room. 

2.  Compute  the  true  value  of  the  velocity  at  the  temperature 
of  the  room,  by  adding  to  the  velocity  at  o°  (332  m.  per  second) 
.6  m.  for  each  degree  above  o°. 

3.  Compute  the  percentage  of  error  of  your  result. 


IX.     LIGHT 

EXERCISE  43.     SHADOWS;    PIN-HOLE   IMAGES; 
LAW  OF  INTENSITY 

References.  —  Adams,  258-262,  304;  Coleman,  332,  334,  337- 
338;  Car.  &  C.,  231-236;  Ches.  G.  &  T.,  274-278,  280-281; 
Hoad.  Br.,  443-445,  447-448  ;  Hoad.  EL,  489-491,  493  ;  Mum- 
per, 190,  192,  194;  Mil.  &  G.,  500-502  ;  Went.  &  H.,  362-364, 
366. 

Apparatus.  —  A  flat  gas  jet,  or  lamp  with  flat  wick  ;  meter  rod 
attached  to  a  board  (Fig.  59),  or  rod  alone  ;  three  screens,  referred 
to  in  tHe  directions  as  A,  B,  and  C,  —  A  is  5  cm.  square  and 


FIG.  59. 


mounted  on  a  wire  (Fig.  59),  B  and  C  are  about  18  or  20  cm. 
square,  B  having  a  broken  horizontal  row  of  small  holes  (Fig.  59), 
and  C  a  small  hole  in  the  center ;  short  metric  rule. 

A  gas  burner  on  a  low  support  should  be  provided  for  this  and 
other  exercises  in  light.  The  low  form  of  Bunsen  burner  can  be 
adapted  to  the  purpose ;  but  a  tip  mounted  on  a  block,  such  as  is 
used  for  the  screens  and  lenses,  is  preferable.  It  will  be  most  con- 

136 


SHADOWS;    PIN-HOLE   IMAGES;    LAW   OF  INTENSITY     137 

venient  to  have  the  screens,  lenses,  spherical  mirrors,  photometer, 
gas  jet,  and  candles  for  the  experiments  in  light  mounted  at  the 
center  of  blocks  of  uniform  size,  in  which  a  groove  is  cut  so  that 
they  fit  loosely  on  a  meter  rod,  placed  on  edge.  The  rod  thus 
serves  as  a  guide  to  keep  the  parts  of  the  apparatus  in  alignment, 
and  the  distances  between  them  will  be  the  distances  between 
the  corresponding  ends  (right  or  left)  of  the  blocks  upon  which 
they  are  mounted.  A  board  100  cm.  long  and  8  or  10  cm.  wide, 
with  the  meter  rod  fastened  to  it,  makes  a  better  support  for  the 
apparatus  (Fig.  59). 

Experiment  ST.  —  To  study  the  formation  of  shadows. 

Experimental  Work. — a.  The  room  must  be  darkened  for  this 
exercise.  Place  the  gas  jet  at  an  end  of  the  meter  rod,  and  place 
the  screens  A  and  B  on  the  rod  about  30  cm.  and  80  cm.  respec- 
tively from  the  same  end,  so  that  the  shadow  of  the  smaller  screen 
falls  on  the  larger.  Turn  the  flame  flatwise  (parallel)  to  the  screens, 
and  adjust  its  height  so  that  the  darker  part  of  the  shadow  (the 
umbra)  covers  all  of  the  lower  holes  on  B,  but  none  of  the  higher 
holes  on  either  side  ;  some,  if  not  all,  of  the  latter  will  then  lie  in 
the  lighter  part  of  the  shadow  (the  penumbra),  which  borders  the 
umbra.  Now  look  toward  the  flame  through  each  of  the  holes  in 
succession,  and  observe  what  portion  of  the  flame,  if  any,  is 
visible  from  these  different  positions.  State  the  connection  between 
what  you  observe  through  each  hole  and  the  character  of  the 
shadow  at  that  place.  Draw  a  diagram  of  a  horizontal  section  of  • 
the  flame,  screens,  and  parts  of  the  shadow  illustrating  your 
explanation. 

b.  Turn  the  flame  edgewise  (perpendicular)  to  the  screens,  and 
note  the  change  in  the  appearance  of  the  shadow  on  B.     Account 
for  this  change,  and  draw  a  section  diagram  to  illustrate. 

c.  Remove  A,  and  in  its  place  hold  a  lead  pencil  vertically. 
Observe  the  shadow  of  the  pencil  on  B,  with  the  flame  turned 
edgewise,  then  flatwise.     With  the  flame  flatwise,  observe  the  vary- 
ing width  of  the  umbra  and  penumbra  as  the  screen  is  moved  up 


138  LIGHT 

to  the  pencil.  Describe  the  observed  changes  in  the  appearance 
of  the  shadow,  and  draw  diagrams  to  illustrate.  (Remember  that 
what  we  commonly  call  a  shadow  is  only  a  cross  section  of  it.  A 
shadow  is  really  the  space  from  which  the  light  is  wholly  or  partly 
excluded  by  an  opaque  body.) 

Experiment  82.  —  To  study  the  formation  of  images  by  small 
openings. 

Experimental  Work. — a.  Place  the  gas  jet,  turned  flatwise, 
a  short  distance  from  the  screen  C  (the  one  with  the  single  hole  at 
its  center),  and  place  the  screen  B  close  behind  C.  The  light 
from  the  jet  that  passes  through  the  hole  in  C  forms  an  image  of 
the  jet  on  B.  Move  B  toward  and  from  C,  and  observe  the  effect 
on  the  size  and  brightness  of  the  image.  Account  for  the  inver- 
sion of  the  image  and  its  change  of  size  when  B  is  moved,  refer- 
ring to  a  diagram  of  a  vertical  section  of  the  apparatus,  the  flame, 
and  the  image. 

Account  for  the  change  in  brightness  when  B  is  moved  away 
from  C. 

b.  Replace  C  with  a  sheet  of  paper  in  which  you  have  made  a 
small  hole  with  the  point  of  your  pencil.  Hold  the  paper  so  that 
the  light  through  this  hole  will  form  an  image  on  J39  and  note  the 
effect  of  gradually  enlarging  the  hole  till  it  is  2  cm.  or  more  in 
diameter.  Describe  and  explain  the  changes  in  the  image  as  the 
hole  is  made  larger. 

Experiment  83.  —  To  find  how  the  intensity  of  light  is  affected 
by  distance. 

Experimental  Work.  —  a.  Since  this  experiment  deals  with  nu- 
merical relations,  measurements  must  be  made  accurately.  Place 
the  screen  B  so  that  it  (not  its  support)  is  exactly  60  cm.  from  the 
center  of  the  gas  jet,  and  place  the  small  screen  A  exactly  midway 
between  them  (i.e.  30  cm.  from  the  center  of  the  flame).  Turn 
the  flame  down  so  as  to  get  as  nearly  as  possible  a  point  source  of 
light  without  losing  the  outline  of  the  shadow  of  A  on  B.  Meas- 


PHOTOMETRY 

ure  the  dimensions  of  A  and  the  dimensions  of  its  shadow  on  B. 
How  do  the  dimensions  of  A  and  of  its  shadow  on  B  compare  ? 
How  do  their  areas  compare  ?  If  A  were  removed,  the  light  which 
now  illuminates  it  would  fall  upon  B  and  would  cover  the  area 
now  occupied  by  the  shadow.  How  would  the  intensity  of  illumi- 
nation on  B  then  compare  with  the  present  illumination  on  A? 
Why?  Does  the  relative  brightness  of  A  and  of  the  illuminated 
part  of  B  seem  to  be  in  agreement  with  this  conclusion?  Both 
screens  are  partly  illuminated  by  light  from  other  sources  than  the 
gas  jet.  (How  do  you  know?)  Does  this  other  light  make  the 
illumination  of  the  screens  more  or  less  nearly  equal  than  would 
be  the  case  if  the  gas  jet  were  the  only  source? 

b.  Repeat  the  experiment  with  A  30  cm.  and  B  90  cm.  from 
the  flame.  Answer  all  the  questions,  changing  them,  where  neces- 
sary, to  agree  with  the  present  distances. 

State  the  general  relation  between  intensity  of  illumination  and 
distance  from  the  source. 

EXERCISE   44.     PHOTOMETRY 

References.  —  Adams,  261-264  ;  Coleman,  338-340 ;  Car.  &  C., 
235-238;  Ches.  G.  £  T.,  281-282  ;  Hoad.  Br.,  447-449;  Hoad. 
£1,494-496;  Mumper,  192-193;  Mil.  &  G.,  502-505;  Went. 
&  H.,  366-367. 

Apparatus.  —  A  Rumford's  or  Bunsen's  photometer  (Figs.  60 
and  61)  ;  i  large  candle  and  5  small  ones;  3  blocks  for  support- 
ing candles  ;  flat  gas  jet  or  lamp  ;  meter  rod. 

[A  Rumford's  photometer,  consisting  of  a  screen  of  \vhite  card- 
board and  a  rod,  each  supported  vertically,  is  the  most  satisfactory 
form  of  photometer  for  elementary  laboratory  work,  as  it  is  least 
affected  by  the  diffused  light  in  an  imperfectly  darkened  room  or 
a  room  in  which  more  than  one  piece  of  apparatus  is  in  use. 
The  box  form  of  the  Bunsen  photometer  is  effective,  but  bulky 
and  rather  troublesome  to  manipulate.  The  author  is  of  the 
opinion  that  laboratory  work  in  photometry  is  hardly  worth  the 


140 


LIGHT 


trouble.  If  a  laboratory  is  not  already  equipped  with  satisfactory 
apparatus  or  a  separate  dark  room  for  this  work,  he  would  recom- 
mend that  such  work  be  omitted,  and  that  the  principles  of 
photometry  be  illustrated  in  the  classroom  only.] 

Method.  —  We  can  make  no  reliable  estimate  of  the  relative 
brightness  of  unequally  illuminated  surfaces,  but  are  able  to  judge 
with  considerable  accuracy  whether  two  adjacent  surfaces,  seen  at 
the  same  time,  are  equally  illuminated ;  hence,  with  all  forms  of 
photometers,  the  distances  of  the  lights  compared  are  adjusted  so 
as  to  give  equal  illumination. 

Rumford's  Photometer.  —  Figure  60  shows  the  adjustment  of 
this  apparatus  in  comparing  the  illuminating  powers  of  a  candle 


FIG.  60. 


and  a  gas  jet.  The  rod  casts  two  shadows  on  the  screen,  one 
being  due  to  the  exclusion  of  the  candle  light,  the  other  to  the 
exclusion  of  the  gas  light.  Each  source  of  light  illuminates  the 
shadow  due  to  the  other;  hence,  when  their  relative  distances 
from  the  screen  are  such  that  the  shadows  are  equally  dark  (i.e. 
equally  illuminated),  we  know  that  the  lights  give  equal  intensity 
of  illumination  at  these  distances ;  and,  knowing  the  law,  we  can 
compute  their  relative  illuminating  powers  from  these  measured 
distances.  Conversely,  if  we  know  the  relative  illuminating  powers 
of  the  two  lights,  the  experiment  demonstrates  the  law.  (This  is 
the  problem  of  Experiment  84.)  The  room  must  be  quite  dark, 
or  other  sources  of  light  will  make  the  shadows  too  faint  for 
comparison. 


PHOTOMETRY 


141 


Bunsen's  Photometer.  —  The  box  form  of  this  photometer  is 
shown  in  Figure  61.  The  box  serves  the  purpose  of  shutting  out 
diffused  light  from  other  sources.  The  essential  part  of  the  photom- 
eter is  a  vertical  screen  of  white  paper,  having  a  translucent  spot 
made  by  applying  a  drop  of  hot  paraffine.  If  the  two  sides  of  the 
paper  are  unequally  illuminated,  the  spot  will  appear  darker  than 
the  rest  of  the  paper  when  viewed  from  the  more  strongly  illumi- 
nated side,  and  lighter  when  viewed  from  the  less  strongly  illu- 
minated side.  The  spot  appears  darker  in  the  first  case  because 
it  reflects  less  light  to  the  eye  than  the  rest  of  the  paper  does ;  in 


FIG.  61. 

the  second  case  it  appears  bright  on  account  of  the  light  it  trans- 
mits from  the  other  side.  When  both  sides  are  equally  illuminated, 
the  spot  nearly  disappears  and  looks  exactly  alike  on  both  sides. 
The  adjustment  of  the  photometer  consists  in  moving  the  screen 
from  side  to  side  along  the  line  between  the  two  lights  that  are 
being  compared,  until  the  position  is  found  where  the  spot  has 
the  same  appearance  from  both  sides.  We  know  then  that  the 
two  lights  give  equal  illumination  at  their  respective  distances. 
The  adjustment  of  the  screen  is  much  more  accurately  made  with 
the  aid  of  two  small  mirrors,  so  placed  that  the  two  sides  of  the 
spot  can  be  seen  in  them  at  the  same  time. 

Experiment  84.  —  To  find  the  relation  between  the  illuminating 
pouters  of  two  lights  and  the  distances  at  which  they  give  equal 
illumination. 

Experimental  Work.  —  Mount  a  small  candle  at  the  center  of 
one  block-  and  four  small  candles  in  a  line  on  another.  With  the 
Rumford  photometer,  place  the  single  candle  at  a  distance  of 


142 


LIGHT 


about  40  cm.  from  the  screen,  and  the  four  candles  at  such  a 
distance  that  the  two  shadows  are  equally  dark.  The  rod  that 
casts  the  shadow  should  be  within  a  few  centimeters  of  the  screen, 
and  the  lights  so  placed  that  the  shadows  are  separated  only  by 
a  narrow  line.  The  line  of  four  candles  should  be  parallel  to  the 
screen.  In  making  the  adjustment,  move  one  of  the  lights  toward 
the  screen  till  one  of  the  shadows  is  lighter  than  the  other,  then 
move  it  away  till  the  same  shadow  is  darker  than  the  other. 
Repeat  several  times,  gradually  diminishing  the  distance  covered 
in  the  to-and-fro  motion,  and  finally  estimate  the  correct  position 
as  closely  as  possible.  With  the  Bunsen  photometer,  place  the 
lights  at  the  ends  of  the  meter  rod,  and  move  the  screen  to  one 
side  till  that  side  of  the  spot  is  darker  than  the  other,  then  back 
again  till  the  other  side  is  darker ;  and  repeat  through  a  gradually 
diminishing  distance  till  you  have  found  the  position  where  the 
two  sides  of  the  spot  look  just  alike. 

Care  must  be  taken  to  see  that  the  five  candles  are  burning 
as  nearly  equally  as  possible ;  for  the  light  from  any  one  of  them 
may  vary,  if  left  to  itself,  50  °/0  or  more  in  the  course  of  a  few 
minutes,  and  the  experiment  is  based  upon  the  assumption  that 
the  four  candles  give  four  times  as  much  light  as  the  single  candle. 
Use  scissors  to  trim  the  wicks  before  adjusting  the  distances,  if 
the  candles  are  burning  unequally. 

When  the  adjustment  for  equal  illumination  has  been  made, 
measure  the  distances  of  the  lights  from  the  screen.  Make  and 
record  two  or  three  trials,  leaving  the  position  of  one  of  the  lights 
unchanged  with  the  Rumford  photometer,  and  the  position  of  both 
lights  unchanged  with  the  Bunsen. 

Data  and  Computations.  —  Let  Pl  denote  the  illuminating  power 
of  the  single  candle  and  Dl  its  average  distance  from  the  screen  ; 
/2  the  illuminating  power  of  the  group  of  four  candles  and  Dz  its 
average  distance.  It  is  assumed  that  P2  =  4  P\-  This  assumption 
may,  however,  be  in  error  by  as  much  as  10  or  15  %,  even  with 
careful  attention  to  the  candles.  Record  as  follows  :  — 


PLANE   MIRRORS  jj* 

Distance  of  single  candle  s-  cmt 

Ditto,  second  trial  —  cm> 

Ditto,  average,  Dl  —  cm> 

Distance  of  group  of  four  candles  =  cm. 

Ditto,  second  trial  =  cm< 

Ditto,  average,  Z>2  =  cm. 

Ratio  of  illuminating  powers  of  the  lights  Pl  -f-  P2  =  .25 

Ratio  of  distances  of  the  lights  D±  -:-  D2  = 

Ratio  of  the  squares  of  the  distances  D?  -~  D/  = 

Percentage  of  difference  between  Pl  -+-  P2  and  Dl  -~  Z>2  =  cf0 

Percentage  of  difference  between  P1  -f-  P2  and  D* -r- D£  =  cj0 

Is  the  difference  between  either  of  these  pairs  of  ratios  within  a 
reasonable  limit  of  experimental  error  (say  15  %)?  If  so,  what  is 
the  answer  suggested  to  the  question  stated  as  the  object  of  the 
experiment? 

Experiment  85.  —  To  measure  the  candle  power  of  a  small 
candle  and  a  gas  jet  or  a  lamp. 

Experimental  Work.  —  a.  Use  the  photometer  to  find  the  ratio 
of  the  illuminating  power  of  a  small  candle  to  the  large  one,  i.e. 
taking  the  large  candle  as  the  standard,  find  the  candle  power  of 
the  small  candle. 

b.  Find  the  candle  power  of  the  gas  jet  or  the  lamp  (which- 
ever is  provided),  when  turned  to  a  moderate  height,  by  compar- 
ing it  with  the  large  candle.  Have  the  flame  turned  flatwise 
toward  the  screen. 

EXERCISE   45.     PLANE   MIRRORS 

References.  —  Adams,  265-266,  304-307;  Coleman,  342-348; 
Car.  &  C.,  239-245  ;  Ches.  G.  &  T.,  283-290;  Hoad.  Br.,  450- 
455  >  Hoad.  EL,  497-503;  Mumper,  195-197;  Mil.  &  G.,  506- 
508,  528-530;  Went.  &  H.,  369-371. 

Apparatus.  —  A  small,  rectangular  plane  mirror,  with  support 
(if  mounted  with  a  free  space  of  about  5  mm.  under  it,  as  shown 


144 


LIGHT 


FIG.  62. 


in  Figure  62,  it  will  serve  for  both  experiments  following)  ;  metric 
rule ;  protractor  ;  pins. 

[In  using  common  mirrors  for  the  study  of  images,  an  error  is 
involved,  due  to  two  refractions  of  the  light  at  the  front  surface. 

These  refractions  diminish  the  dis- 
tance of  the  image  by  about  two 
thirds  the  thickness  of  the  mirror. 
Hence  thin  mirrors  are  to  be  pre- 
ferred. The  error  is  reduced  one 
half,  if,  in  locating  the  image  by 
the  method  of  Experiment  87,  the 
pin  that  is  made  to  coincide  with 
the  image  is  viewed  through  an  unsilvered  portion  of  the  glass. 
The  error  will  be  entirely  avoided  if  the  front  surface  of  a  piece  of 
plate  or  window  glass  is  used  as  the  reflecting  surface.  The  image 
thus  obtained  will  be  quite  distinct  if  the  glass  is  backed  with  black 
paper  or  cloth.  Since  both  surfaces  reflect,  two  images  will  be 
seen.  The  rear  image  will  disappear  and  the  other  will  be  more 
distinct  if  the  back  of  the  glass  is  painted  black.] 

Experiment  86.  —  To  find  the  position  of  a  point  image  in  a 
plane  mirror  by  sight  lines ;  and  to  find  the  relation  between  the 
position  of  the  point  and  its  image,  and  the  relation  between  the 
angles  of  incidence  and  reflection. 

Method.  —  A   sheet   of   paper   is      

•  laid  on  the  table,  and  the  mirror 
placed  on  it  in  a  vertical  position 
marked  by  the  line  AB  (Fig.  63). 
A  pin  is  stuck  in  a  vertical  position 
at  O  in  front  of  the  mirror,  and  the 
point  where  it  pierces  the  paper  is 
taken  as  the  object  whose  image  in 
the  mirror  is  to  be  located.  If  this  image  has  a  fixed  position 
behind  the  mirror,  all  lines  drawn  on  the  paper  in  front  of  the 
mirror  and  extending  in  the  direction  of  the  image  will  intersect 


FIG.  63. 


PLANE   MIRRORS 


145 


at  the  position  of  the  image  when  produced;  and  this  position 
will  be  determined  by  the  intersection  of  any  two  such  lines. 
Lines  thus  drawn  are  called  sight  lines,  i.e.  lines  along  which  the 
observer  sights  toward  the  image.  A  sight  line  is  determined  by 
means  of  two  pins,  placed  vertically  several  centimeters  apart 
(as  at  C  and  D  in  the  figure)  and  exactly  in  line  with  the  image 
of  O,  the  pin  at  C  being  placed  first,  at  any  point  near  the  mirror 
and  on  either  side  of  O.  A  line  is  then  carefully  drawn  with  a 
rule  and  a  sharp  pencil  through  the  points  C  and  Z>,  and  pro- 
duced after  the  mirror  is  removed. 

Experimental  Work.  —  Draw  a  line  AB  about  10  cm.  long  on  a 
large  sheet  of  paper,  leaving  a  space  of  not  less  than  8  cm.  on 
each  side  of  it.  Stand  the  mirror  so  that  the  plane  of  its  reflect- 
ing surface  passes  exactly  through  this  line.  In  doing  this,  look 
vertically  down  along  the  reflecting  surface.  (The  reflecting  sur- 
face of  a  common  mirror  is,  of  course,  the  rear  surface.  If  unsil- 
vered  glass  is  used,  either  with  or  without  the  back  painted  black, 
its  front  surface  is  the  reflecting  surface.  If  the  back  surface  is 
not  painted  or  ground,  it,  too,  will  cause  an  image,  slightly 
farther  back  than  the  first ;  but  this  image  is  to  be  disregarded.) 
Stick  a  pin  vertically  3  or  4  cm.  in  front  of  the  mirror,  and  mark 
the  point  where  it  pierces  the  paper  O.  This  point  is  the  object 
whose  image  is  to  be  located. 

Draw  four  sight  lines  directed  accurately  toward  the  image,  and 
determined  in  the  manner  described  above,  two  of  them  lying  on 
each  side  of  O.  In  sighting,  place  the  eyes  on  a  level  with  the 
paper,  close  one  of  them,  and  have  the  pins  parallel.  The  sight 
lines  should  all  make  wide  angles  with  each  other ;  since,  if  any 
two  are  nearly  parallel,  a  slight  error  in  the  direction  of  either 
will  make  a  relatively  large  error  in  their  point  of  intersection.  If 
necessary  in  order  to  get  wide  angles,  the  mirror  may  be  shifted 
parallel  to  itself  along  the  line  AB. 

Remove  the  mirror  and  produce  the  sight  lines  on  the  other 
side  of  AB.  If  the  image  has  the  same  position  when  viewed 
COLEMAN'S  NEW  MANUAL  —  10 


146  LIGHT 

from  different  directions,  the  sight  lines,  if  accurately  determined, 
will  all  intersect  at  the  same  point.  Repeat  the  experiment  if  the 
points  of  intersection  do  not  coincide  within  2  mm.  With  care- 
ful work  they  should  coincide  within  i  mm. 

Mark  the  point  of  intersection  of  the  sight  lines  /.  Draw  the 
line  OI.  Measure  with  the  protractor,  and  record  in  the  figure, 
one  of  the  angles  formed  by  AB  and  OI.  What  should  this  angle 
be?  Measure  the  segments  of  OI  formed  by  its  intersection  with 
AB,  and  record  in  the  figure.  How  should  these  segments 
compare  ? 

It  is  evident  that,  when  you  were  looking  along  any  one  of  the 
sight  lines,  the  light  by  which  you  saw  the  image  came  to  the  eye 
along  that  line,  having  been  reflected  by  the  mirror  at  the  point 
where  the  sight  line  meets  AB.  Mark  this  point  N.  Draw  the 
line  ON,  representing  the  incident  ray;  and  draw  the  perpen- 
dicular to  AB  at  N  (using  the  protractor).  Measure  with  the 
protractor,  and  record  in  the  figure  the  angles  of  incidence  and 
reflection.  Repeat  this  construction  and  measurement  for  one 
other  sight  line.  How  nearly  do  the  constructed  angles  of  inci- 
dence and  reflection  agree  with  the  law?  With  careful  work  the 
error  will  be  less  than  i°. 

The  sheet  on  which  this  work  is  done  may  be  pasted  in  your 
record  book,  or  an  accurate  copy  of  the  figure  made  by  placing 
the  sheet  on  the  one  to  which  the  figure  is  to  be  transferred,  and 
pricking  two  pin  points  through  to  mark  the  position  of  each 
line. 

Experiment  87.  —  To  find  the  position  of  a  point  image  in  a 
plane  mirror  by  direct  observation. 

Preliminary  Study  (to  precede  the  laboratory  hour).  —  Hold  a 
pencil  at  arm's  length,  pointing  upward,  in  one  hand,  and  a  sec- 
ond pencil  at  about  two  thirds  that  distance,  pointing  downward, 
in  the  other  hand.  Bring  the  points  of  the  pencils  into  line  with 
one  eye,  the  other  eye  being  closed.  The  points  will  seem  to 
touch,  although  they  are  really  15  cm.  or  more  apart.  Without 


PLANE   MIRRORS 


147 


moving  either  pencil,  look  at  them  with  the  other  eye,  closing  the 
first,  and  note  the  change  in  the  apparent  positions  of  the  pen- 
cils. Repeat,  closing  first  one  eye,  then  the  other,  with  the  pen- 
cils in  line  with  each  eye  in  turn,  until  you  are  familiar  with  the 
effects,  and  have  discovered  the  reason  for  the  apparent  shifting 
of  the  pencils  when  you  change  the  eye  with  which  you  look. 
Now  look  with  both  eyes,  first  at  the  nearer  pencil,  then  at  the 
farther  one,  and  note  that  when  you  are  looking  at  either  pencil, 
the  other  appears  double ;  note  also  that  while  looking  with  both 
eyes,  there  is  no  misjudgment  of  distances.  Look  again  with 
each  eye  in  turn,  as  you  gradually  move  either  pencil  toward  the 
other ;  and  note  that  the  apparent  shifting  of  the  pencils  from  side 
to  side  becomes  less,  and  ceases  only  when  the  points  are  actually 
in  contact. 

Familiarity  with  these  phenomena  of  vision  will  be  of  great 
assistance  in  the  following  experiment,  and  in  several  later  ones  as 
well,  where  the  work  has  to  do  with  the  actual  position  of  images. 
The  apparent  displacement  of  an  object,  due  to  a  change  in  the 
position  from  which  it  is  viewed,  is  called  parallax. 

Experimental  Work.  —  Draw  a  line  AB  across  the  middle  of  a 
large  sheet  of  paper,  and  stand  the  mirror  with  its  reflecting  sur- 
face vertically  over  it.  Stick  a  pin  in  a  vertical  position  at  a  dis- 
tance of  several  centimeters  in  front  of  the  mirror.  With  the  eyes 
just  above  the  level  of  the  table,  look  under  the  mirror  at  a  second 
pin,  held  vertically  in  the  fingers  behind  the  mirror ;  and  place 
this  pin  where  it  appears  to  coincide  with  the  image  of  the  pin  in 
front.  In  doing  this,  look  with  both  eyes,  and  move  the  head  into 
various  positions.  When  the  pin  is  correctly  placed,  it  will  accu- 
rately fit  the  image  from  all  points  of  view. 

When  the  image  is  correctly  located,  draw  a  line  connecting  it 
with  the  object.  Measure  and  record  the  segments  into  which 
this  line  is  divided  by  AB,  and  the  angle  between  the  lines.  If 
time  remains,  see  if  you  can  get  more  accurate  results  by  further 
trials,  placing  the  object  in  a  different  position  each  time, 


148  LIGHT 

EXERCISE   46.     MULTIPLE   IMAGES 
(INVENTIVE) 

References.  —  Adams,  308-309  ;  Coleman,  349  ;  Car.  &  C., 
246-247;  Hoad.  Br.,  456-458;  Hoad.  EL,  504-506;  Mil.  &  G., 
532  ;  Went.  &  H.,  373. 

Experiment  88.  —  To  study  the  formation  of  images  by  multiple 
reflection  from  two  plane  mirrors. 

Apparatus.  —  Two  plane  mirrors,  each  with  a  support  to  hold  it 
in  a  vertical  position ;  rule  ;  candle,  mounted  ;  some  small  object 
having  right  side  distinguishable  from  left  and  front  from  back ;  etc. 

Suggestions.  —  In  performing  this  experiment  it  is  necessary  to 
bear  in  mind  that  the  reflected  light  travels  from  the  direction  of 

the  image,  just  as  if  the 
image  were  the  real  source. 
The  principal  points  that 
come  within  the  scope  of 
the  experiment  are  as  fol- 
lows :  — 

i.  With  the  mirrors  at  a 
given  angle,  to  note  the 
number  of  images  formed 
and  their  exact  location  with 
respect  to  the  object,  the 
FIG.  64.  mirrors,  and  the  images  of 

the  mirrors. 

2.  To   determine    the   number   of  reflections   by  which  each 
image  is  formed,  and  the  order  in  which  these  reflections  occur 
(/>.  from  which  mirror  first). 

3.  To  account  for  the  number  and   position   of  the   images, 
from  the  known  reflections  of  the  light  and  the  law  of  reflection. 

4.  To  observe  which  of  the  images  have  their  right  and  left 
sides  reversed  and  which  have  not,  and  to  determine  why. 


THE  CONCAVE   MIRROR 

5.  To  determine  the  path  of  a  ray  of  light  from  the  object  to 
the  eye,  in  viewing  any  one  of  the  images  from  a  given  position. 

6.  To     construct     dia- 
grams  illustrating  the  an-       I    «LN 

swers  to  these  questions.          7, x" 

Make  a  study  of  these       l   Q^>,x      Xs 
questions  and  of  others  that     — 
may  occur  to  you,  devising 
methods  of  procedure  for 
yourself.    The  mirrors  may      |f 
be  at  any  angle,  an  angle 
of   90°  being  the  simplest 
case.     The  case  of  parallel       i 
mirrors  should  be  included.      ~v 


•-ni  r-  9f'  FlG.  6s. 

Ihe  accompanying  figures 

will  afford  suggestions  as  to  the  character  of  the  diagrams.     If  a 

kaleidoscope  is  provided,  investigate  its  construction  and  action. 

EXERCISE   47.     THE   CONCAVE   MIRROR 

References. — Adams  310-316;  Coleman,  350-355  ;  Car.  &C., 
249-255;  Ches.  G.  &  T.,  295-298;  302-305;  Hoad.  Br.,  460- 
466  ;  Hoad.  EL,  507-512  ;  Mumper,  198;  Mil.  and  G.,  538-545  ; 
Went.  &  H.,  374-376,  379- 

Experiment  89.  —  To  find  the  focal  length  and  radius  of  curva- 
ture of  a  concave  mirror,  and  to  study  the  formation  of  real  and 
virtual  images  by  it. 

Apparatus.  —  Concave  mirror ;  meter  rod  ;  mounted  candle ; 
cardboard  screen. 

[A  silvered  mirror  of  glass  having  a  diameter  of  10  or  n  cm. 
is  adapted  to  this  experiment.  These  can  be  obtained  in  a 
wooden  frame  with  a  handle,  and  also  in  a  light  metal  frame, 
which  is  preferable.  It  will  be  found  convenient  to  have  them 
mounted  on  blocks,  uniformly  with  the  screens,  lenses,  etc.,  as 
suggested  under  Exercise  43.] 


1 50  LIGHT 

Experimental  Work.  —  a.  Hold  the  mirror  in  the  sunlight  and 
facing  exactly  toward  the  sun,  and  focus  the  light  on  a  piece  of 
paper.  In  doing  this,  hold  the  paper  a  little  to  one  side,  so  as 
not  to  cut  off  the  light  from  the  mirror ;  turn  the  mirror  so  that 
the  reflected  light  falls  upon  the  paper  and  move  the  paper  toward 
or  from  the  mirror  into  the  position  where  the  spot  of  light  is  the 
smallest.  The  spot  is  an  image  of  the  sun,  and  if  the  adjustment 
is  right,  it  will  be  round. 

b.  Stand  the  mirror  on  the  table  near  a  window,  and  turn  it 
facing  toward  some  distant  object,  as  a  house  or  a  tree,  at  least 
200  ft.  away.     Stand  the  cardboard  screen  on  the  table  in  front 
of  the  mirror  and  a  little  to  one  side  of  the  direct  line  between 
the  minor  and  the  object  (in  order  not  to  intercept  the  light),  and 
adjust  its  distance  from  the  mirror  till  the  image  of  the  distant 
object  is  sharply  denned  upon  it.     If  the  weather  is  not  too  cold, 
raise  the  window  in  making  this  adjustment,  for  the  light  is  dis- 
torted by  the  wavy  surfaces  of  common  window  glass,  and  this 
makes  perfect  focusing  impossible.      Measure  the  distance  from 
the  image  to  the  mirror.     This  is  the  focal  length  f  of  the  mirror 
(the  rays  from  any  point  of  the  object  being  sensibly  parallel). 

c.  Move  the  screen  a  little  to  one  side,  leaving  it  in  the  plane 
of  the  image  and  near  it  so  as  to  mark  its  position.     Place  the 
head  very  nearly  in  line  between  the  mirror  and  the  object,  at  a 
distance  of  about  a  meter  from  the  mirror,  and  look  toward  the 
mirror  at  the  place  in  the  air  beside  the  screen,  where  the  image  is. 
If  this  is  correctly  done,  the  image  will  be  very  distinctly  seen  in 
its  real  position  in  front  of  the  mirror.     It  is  difficult  for  the  be- 
ginner to  avoid  looking  beyond  the  image  into  the  mirror ;    in 
which  case  the  image  will  appear  to  be  in  the  mirror  and  will  be 
blurred,  — just  as  the  finger  appears  blurred  and  double  when  you 
hold  it  before  you  and  look  at  something  beyond  it.      If  you  are 
unsuccessful  after  a  brief  trial,  pass  this  for  the  present,  and  try 
again  after  finishing  the  exercise. 

d.  The  remainder  of  the  exercise  requires  a   darkened  room. 
Place  the  lighted  candle  at  one  end  of  the  meter  stick,  and  stand 


THE   CONCAVE    MIRROR  151 

the  mirror  at  the  other  end.  Place  the  eyes  on  a  level  with  the 
candle,  and  look  past  it  toward  the  mirror.  A  number  of  real  and 
inverted  images  of  the  candle  will  be  seen  in  line  between  it  and 
the  mirror.  The  one  that  is  the  largest,  the  farthest  from  the 
mirror,  and  the  brightest  is  the  one  that  is  formed  by  a  single 
reflection  at  the  concave  silvered  surface,  and  is  the  one  to  be 
studied.  The  others  are  due  to  multiple  reflections  within  the 
mirror.  Turn  or  tip  the  mirror  a  little,  if  necessary,  to  bring  the 
images  into  line  with  the  candle,  and  be  careful  to  find  the  princi- 
pal one.  Ignore  the  others.  Move  the  candle  along  the  meter 
rod  till  the  tip  of  the  flame  coincides  with  the  tip  of  the  image, 
turning  or  tilting  the  mirror,  if  necessary.  Object  (the  tip  of  the 
flame)  and  image  are  now  at  the  center  of  curvature  of  the  mirror. 
(Why?)  Measure  their  distance  from  the  mirror.  This  is  the 
radius  of  curvature  r.  Compare  r/2  wiihf,  found  in  paragraph  b. 

e.  Starting  with  the  candle  at  the  center  of  curvature,  carry  it 
slowly  across  the  room  as  far  as  you  can  from  the  mirror,  while 
your  companion,  standing  near  the  mirror,  observes  the  simul- 
taneous change  of  size  and  position  of  the  image.  Measure  the 
distance  of  the  image  from  the  mirror  when  the  object  is  farthest 
away,  focusing  the  image  on  the  screen  for  the  purpose,  if  found 
more  convenient.  Compare  this  distance  with  /.  What  would 
be  the  final  position  of  the  image  if  the  object  were  carried  farther 
away  indefinitely? 

/  Again  starting  with  the  candle  near  the  center  of  curvature, 
move  it  slowly  toward  the  principal  focus,  meanwhile  keeping 
watch  of  the  changing  size  and  position  of  the  image  by  focusing 
it  on  the  screen.  Continue  till  the  image  is  focused  upon  a 
distant  wall  of  the  room,  or  as  far  away  as  it  can  be  seen.  With 
this  adjustment,  measure  the  distance  of  the  candle  from  the 
mirror,  and  compare  with  the  distance  of  the  image  when  the 
candle  was  at  its  greatest  distance.  If  the  candle  were  moved  up 
to  the  principal  focus,  where  would  the  image  be  ? 

g.  Move  the  candle  from  the  principal  focus  toward  the  mirror, 
while  observing  the  change  in  the  size  and  position  of  the  image, 


152  LIGHT 

which  is  now  virtual,  erect,  and  behind  the  mirror.  (A  faint  vir- 
tual image  of  constant  size  will  also  be  seen.  This  is  due  to  par- 
tial reflection  from  the  front  surface  of  the  mirror,  which  is  plane.) 
Estimate  the  relative  distances  of  image  and  object  from  the 
mirror. 

Discussion.  —  From  a  study  of  the  text  you  will  learn  how  the 
facts  observed  in  this  exercise  result  from  the  law  of  reflection 
and  the  curvature  of  the  reflecting  surface.  The  text  also  dis- 
cusses the  construction  of  explanatory  diagrams.  From  a  study 
of  the  text  and  the  results  of  the  experiment,  find  the  answers  to 
the  following  questions  :  — 

1.  What  happens,  after  reflection,  to  the  diverging  cone  of  light 
that  falls  upon  the  mirror  from  any  one  point  of  the  object  (a) 
when  the  distance  of  the  object  is  greater  than  the  focal  length ; 
(b)    less  than  the  focal  length ;   (c)   equal  to  the  focal  length? 

2.  What  behavior  of  the  reflected  light  gives  rise  to  (a)  a  real 
image  ;  (b)  a  virtual  image  ?     (Remember  that  a  focus  is  a  point, 
and  that  images  have  size.     Be  definite  in  your  answer.) 

3.  Under  what  conditions  is  (a)  a  real  image  formed;   (b)  a 
virtual  image? 

4.  With  rule  and  compass  draw  accurate  figures  showing  the 
size  and  position  of  the  image  formed  by  a  concave  mirror  — 

When  the  object  is  large  and  at  a  relatively  great  distance  (illus- 
trating paragraph  b  of  the  experiment). 

When  the  object  is  a  point  at  the  center  of  curvature  (illus- 
trating paragraph  d\ 

When  the  object  is  beyond  the  center  of  curvature,  but  not  at  a 
great  distance  (illustrating  paragraph  e). 

When  the  object  is  between  the  principal  focus  and  the  center 
of  curvature  (illustrating  paragraph/). 

When  the  object  is  only  slightly  nearer  the  mirror  than  the 
principal  focus  (illustrating  paragraph  £•). 

When  the  distance  of  the  object  from  the  mirror  is  about  \  the 
focal  length  (illustrating  paragraph^). 


PHENOMENA   DUE  TO   REFRACTION  153 

Use  the  same  radius  of  curvature  in  all  the  above  figures,  and 
in  all  but  the  first  two  represent  the  object  by  an  arrow  of  the 
same  length.  The  object  cannot  be  represented  in  the  first  dia- 
gram, being  too  far  away  and  too  large  to  be  represented  to 
scale. 

EXPERIMENT  48.    PHENOMENA  DUE  TO  REFRACTION 

References. — Adams,  267-268;  Coleman,  358-359;  Car.  & 
C.,  256-257;  Ches.  G.&T.,  310-311  ;  Hoad.  Br.,  467-470,  474  ; 
Hoad.  EL,  515-518,  522;  Mumper,  200;  Mil.  &  G.,  510;  Went. 
&  H.,  381-382. 

Experiment  90.  —  To  study  the  refraction  of  light  in  passing  from 
glass  into  air,  and  the  apparent  displacement  of  objects  resulting 
from  such  refraction. 

Apparatus.  —  A  rectangular  piece  of  thick  plate  glass,  ground 
and  polished  on  two  opposite  ends;  glass  prism  with  flat  ends 
and  wide  faces  ;  rule  ;  pins. 

Experimental  Work.  —  a.  Stand  the  prism  on  end  on  this  page, 
and  look  at  the  printing  through  it.  Note  the  apparent  elevation 
of  the  part  of  the  page  seen  through  the  prism.  Estimate  the 
ratio  of  the  real  length  of  the  prism  to  its 
apparent  length,  as  you  look  through  it.  Lay 
the  piece  of  plate  glass  on  the  page,  and 
observe  whether  there  is  a  similar  apparent 
elevation  of  the  part  seen  through  it.  Stand 
the  plate  on  one  of  its  polished  ends  and 
look  down  through  the  width  of  the  glass  at 
the  printing.  Result? 

b.   Lay  a  sheet  of  paper  on  the  table,  and 


lay  the  glass  plate  on  it  near  the  farther  end  FlG  66 

(Fig.  66),  with  its  polished  ends  at  front  and 
rear.     Stick  pins  vertically  at  A,  B,  and  C,  close  to  the  glass  — 
A  at  the  middle  of  the  farther  end,  B  and  C  about  2  cm.  apart 


154  LIGHT 

at  the  front  end.  Place  the  eyes  just  above  the  level  of  the  table, 
close  one  of  them,  and  move  the  other  into  line  with  B  and  the 
apparent  position  of  A,  seen  through  the  glass.  Place  another  pin 
exactly  in  this  line,  5  or  6  cm.  toward  the  eye  from  B ;  and  mark 
its  position  D.  The  line  DB  indicates  the  direction  in  which  A 
is  seen  through  the  glass,  when  the  eye  is  in  its  present  position. 
Obviously,  the  light  by  which  A  is  seen  from  this  position  emerges 
from  the  glass  at  B  (since  B  appears  to  be  in  line  with  A),  and 
traverses  the  path  BD  to  the  eye.  Its  path  through  the  glass  is 
along  the  straight  line  AB.  Since  A,  B,  and  D  are  not  in  a 
straight  line,  it  follows  that  the  light  undergoes  a  change  of  direc- 
tion (refraction)  at  B.  It  is  important  to  note  that  A  is  seen  in 
the  direction  from  which  the  light  is  traveling  as  it  enters  the  eye, 
—  a  general  truth  that  has  become  familiar  in  the  study  of  images 
formed  by  reflection.  In  fact,  what  is  seen  through  the  glass  is  an 
image  of  A  formed  by  refraction. 

In  the  same  way  place  a  pin  (at  E  in  the  figure)  in  line  with 
C  and  the  apparent  position  of  A. 

Draw  the  outline  of  the  glass  plate  pn  the  paper ;  remove  the 
plate;  draw  the  lines  DB  and  EC,  and  produce  them  as  dotted 
lines  to  their  point  of  intersection;  letter  this -point  A1 ;  draw 
the  lines  AB  and  AC ';  and  place  arrowheads  on  the  parts  of 
the  broken  lines  ADB  and  ACE.  These  broken  lines  with  the 
arrowheads  represent  actual  paths  of  light  from  A  through  the 
glass  and  into  the  air;  the  dotted  lines  AB  and  A'C  indicate 
apparent  paths  of  light  from  the  image  A'. 

Is  the  refraction  to  the  right  or  the  left  at  Bt  Does  this  cause 
A  to  appear  to  the  right  or  the  left  of  its  true  direction  ?  Answer 
the  same  questions  for  the  refraction  at  C. 

c.  Replace  the  glass  plate  in  its  former  position,  and  find  the 
apparent  direction  and  position  of  A  when  viewed  through  the 
glass  along  the  line  perpendicular  to  the  front  surface.  Is  its 
apparent  position  the  same  as  when  viewed  along  the  lines  DB 
and  £C?  (Answer  from  direct  observation  with  one  eye  and 
also  with  both.)  Does  it  appear  to  be  to  the  right,  to  the  left,  or 


PHENOMENA   DUE  TO   REFRACTION 


155 


in  its  real  direction?  What  does  this  indicate  concerning  the 
refraction  (bending)  of  the  ray  that  is  perpendicular  to  the  surface 
of  the  glass? 

d.  Move  the  head  to  one  side  so  as  to  view  A  more  obliquely 
through  the  glass  than  DB  or  EC,  and  note  the  change  in  its 
apparent  position,  using  both  eyes  for  the  observation  and  without 
placing  pins.  State  the  result. 

Copy  the  figure  accurately  or  paste  the  sheet  in  your  record 
book. 

Experiment  91.—  To  study  the  apparent  displacement  of  objects 
under  water,  due  to  refraction  at.  the  surface. 

Apparatus. — Glass  jar,  preferably  rectangular;  bit  of  tin  or 
other  small  object  that  sinks  in  water ;  large  jar  of  water ;  beaker ; 
rule ;  mop  cloth. 

Experimental  Work.  —  a.  Pour  water,  a  little  at  a  time,  into 
the  smaller  jar,  while  looking  down  at  the  bottom  of  the  jar 
through  the  water ;  and  observe  the  apparent  eleva- 
tion of  the  bottom  above  the  level  of  the  table  top. 
How  does  the  apparent  elevation  of  the  bottom 
change  as  the  depth  of  the  water  increases? 
Estimate  the  ratio  of  the  real  depth  of  the  water 
to  its  apparent  depth  as  you  look  vertically  down 
through  it.  Does  this  ratio  appear  to  change  or 
to  remain  constant  as  you  increase  the  depth  of 
the  water?  Figure  67  represents  a  pencil  of  light 
from  a  point  of  the  bottom.  Copy  and  complete 
the  figure  so  as  to  explain  the  apparent  elevation 
of  the  bottom.  Represent  the  apparent  path  of 
light  by  a  dotted  line. 

b.  Fill  the  jar  nearly  full  of  water.  With  the  rule  held  exactly 
vertical,  gradually  lower  an  end  of  it  into  the  water,  observing  any 
change  in  the  apparent  length  of  the  immersed  portion,  when 
viewed  through  the  surface  of  the  water.  Repeat  the  observation, 


FIG.  67. 


156 


LIGHT 


raising  and  lowering  the  rule  several  times.  Does  the  immersed 
portion  appear  to  be  in  its  real  direction  (vertical)  or  does  it 
appear  to  be  oblique?  Does  the  appearance  of  the  immersed 
portion  indicate  an  apparent  oblique  or 
vertical  displacement  of  any  point  from  its 
real  position?  Copy  and  complete  Figure  68 
so  as  to  explain  the  apparent  displacement 
of  the  immersed  end  of  the  rule. 

c.  Observe  any  change  in  the  appearance 
of  the  immersed  portion  of  the  rule,  held 
in  a  fixed  vertical  position,  as  you  view  it 
more  and  more  obliquely  through  the  sur- 
face of  the  water,  gradually  lowering  the 
head  till  the  eyes  are  nearly  on  a  level 
with  the  surface.  Draw  a  figure  represent- 


FIG.  68. 


ing  and  explaining  the  appearance, 
when  the  line  of  sight  is  very 
oblique. 

d.  Hold   the   rule   or    a   pencil 
oblique    and    partly    immersed    in 
water,  and  note  the  apparent  length 
and  direction  of  the  immersed  por- 
tion as   seen  through  the   surface. 
Copy  Figure  69   and  complete  it, 
showing   the  apparent  position   of 
the  immersed  part  of  the  pencil. 

Pupils  often   confuse  the  actual 
direction  of  bending  of  the   light 
with  the  apparent  direction  of  bend- 
ing of  the  object.     Referring  to  your  completed  copy  of  Figure 
69,  show  the  relation  between  these  directions. 

e.  Drop  the  piece  of  tin  (or  other  small  object)  into  the  jar  of 
water,  and  look  down  at  it  while  disturbing  the  water  with  your 
finder.     Describe  and   explain  the  effect  of  the  motion  of  the 
Surface. 


FIG.  69. 


SNELL'S    LAW  OF   REFRACTION 


157 


EXERCISE   49.      SNELL'S    LAW   OF    REFRACTION; 
INDEX   OF   REFRACTION    OF   GLASS 

References.  —  Adams,  268-270;  Coleman,  360-362;  Car.  & 
C,  258-260;  Ches.  G.  &  T.,  312;  Hoad.  Br.,  468-471  ;  Hoad. 
EL,  515-519;  Mumper,  202;  Mil.  &  G.,  523-525;  Went.  &  H., 
381. 

Apparatus — Rectangular  piece  of  thick  plate  glass,  ground 
and  polished  on  two  opposite  ends,  and  having  scratches  perpen- 
dicularly across  the  polished  ends  at  A,  JB,  C,  and  O  (Fig.  70) ; 
pencil  compass ;  metric  rule  ;  pins. 

Experiment  92.  —  To  study  the  relation  between  the  directions  of 
the  incident  and  refracted  rays  for  different  angles  of  incidence; 
and  to  find  the  index  of  refraction  of  a  piece  of  plate  glass. 

CAUTION.  — In  this  experiment  the  numerical  values  are  obtained 
from  a  diagram,  which  must  therefore  be  constructed  as  accurately 
as  possible.  Points  are  to  be  located  by  means  of  minute  dots, 
lines  drawn  very  thin  with  a  rule  and  sharp  pencil,  perpendiculars 
accurately  at  90°,  and  distances  measured  to  tenths  of  a  milli- 
meter. A  pupil  who  has  had  practice  in 
mechanical  drawing  should  be  able  to  get 
results  agreeing  with  the  law  within  i  %  ', 
for  others  an  accuracy  of  2  %  is  very  good 
and  an  error  of  3%  satisfactory. 

Experimental  Work.  —  Have  the  pencil 
very  sharp,  and  keep  it  so.  Draw  a  thin 
straight  line  MN  (Fig.  70)  across  the 
middle  of  a  large  sheet  of  paper,  and  lay 
the  glass  plate  on  it  with  one  of  the 
polished  ends  exactly  at  the  line,  as  shown 
in  the  figure.  The  plate  should  have 
scratches  perpendicularly  across  the  polished  ends  at  A,  B,  C, 
and  O.  Locate  the  exact  position  of  these  scratches  on  the  paper 
by  minute  dots.  If  there  are  not  scratches  on  the  glass,  stick  pins 


ABC 


FIG.  70. 


LIGHT 


vertically  at  these  points,  close  to  the  glass.  The  glass  must  be 
left  exactly  in  this  position  until  pins  have  been  located  at  D,  E, 
and  F,  as  follows :  — 

Place  the  eyes  on  a  level  with  the  table,  close  one  of  them, 
and  place  a  pin  near  the  front  edge  of  the  paper  exactly  in  line 
with  the  scratch  (or  pin)  at  O  and  the  image  of  the  scratch  at  A. 
Letter  this  point  D.  Similarly,  locate  a  pin  at  E  in  line  with  O 
and  the  image  of  B,  and  another  at  F  in  line  with  O  and  the 
image  of  C. 

Remove  the  plate  and  draw  very  accurately  the  broken  lines 
DO  A,  EOB,  and  FOC,  extending  them  in  both  directions  to 
the  edge  of  the  paper.  To  distinguish  the  different  incident 
and  the  corresponding  refracted  rays,  place  a  single  arrowhead 
on  DO  and  on  OAy  two  arrowheads  on  E  O  and  on  OB,  and 
three  on  FO  and  on  OC. 

Fold  a  straight  edge  of  a  sheet  of  paper  to  form  an  accurate 
right  angle,  and  use  it  to  erect  a  perpendicular  to  MN  at  O. 

(Do  this  with  the  great- 
est care.)  Letter  this 
perpendicular  X Y. 

Use  the  pencil  com- 
pass to  describe  a  circle 
with  O  as  a  center  and 
a  radius  of  8  cm.  or 
more.  From  the  six 
points  of  intersection  of 
this  circumference  with 
the  lines  representing 
the  incident  and  re- 
fracted rays,  drop  per- 

FlG  pendiculars   to  XY,  as 

shown    in    Figure    71. 

Let  Pl9  P2,  and  Pz  denote  the  perpendiculars  constructed  for  the 
three  refracted  rays,  and  /V>  ^V>  and  P3'  the  perpendiculars  for 
the  corresponding  incident  rays.  Measure  these  perpendiculars, 


SNELL'S    LAW   OF    REFRACTION 


159 


estimating  carefully  the  tenths  of  a  millimeter,  and  record  their 
lengths  beside  them. 

Paste  or  copy  this  figure  in  your  record  book. 

Data  and  Computations.  —  Compute  the  ratios  P^/PJ,  RJPJ, 
and  Ps/P3f  to  three  decimal  places,  and  find  the  percentage  of 
difference  between  the  greatest  and  the  least  of  them.  According 
to  the  law  of  refraction,  they  should  be  equal. 

Any  one  of  these  ratios  is  an  experimental  value  of  the  index 
of  refraction  of  the  glass  plate,  and  their  average  is  to  be  taken 
as  the  value  of  this  quantity  as  given  by  your  experiment.  Com- 
pute it. 

Discussion SnelPs    Law,  as   commonly  stated,   involves   the 

use  of  the  term  "  sine  of  an  angle."     In  any  right  triangle  the  ratio 

of  either  leg  to  the  hypothenuse 

is  called  the  sine  of  the  angle 

opposite  to  that  leg.      Thus  in 

Figure   72   the   sine  of  angle  A 

is     BC/AB    or    ffC/Aff     or 

B"C"/AB"  (all  of  which  ratios 

are  equal,  since  the  triangles  are 

similar),  and  the  sine  of  angle  B 

is  AC/AB.     The  usual  form  of 

writing  this  is  sine  A  =  BC/AB,  and  sine  B  =  AC/AB.     The 

sine  of  an  angle  increases  as  the  angle  increases  from  o°  to  90°,  but 

they  do  not  increase  proportionally.     In    other  words,  while  the 

greater  of  two  acute  angles  always  has  the  greater  sine,  the  angles 

and  the  sines  are  not  in  proportion. 

Let  the  radius  of  the  circle  in  Figure  71  be  denoted  by  R  ;  then 
the  sine  of  the  smallest  angle  of  incidence  is  P\/R,  and  the  sine 
of  the  corresponding  angle  of  refraction  is  Pi/R.  The  ratio  of 
the  sine  of  the  angle  of  incidence  to  the  sine  of  the  angle 
of  refraction  is  therefore  P^/R  :  P\/R,  or  P\/P^.  If  we  suppose 
the  light  to  be  traveling  from  air  to  glass  (reversing  the  arrow- 
heads in  your  figure),  the  angles  of  incidence  and  refraction  will 


B" 

FIG.  72. 


160  LIGHT 

simply  be  interchanged.  We  shall  then  have  as  the  ratio  of 
the  sine  of  the  angle  of  incidence  to  the  sine  of  the  angle 
of  refraction  PJP±,  Py/P*,  and  P3/P3'  for  the  three  cases, 
respectively,  and  we  have  learned  that  these  ratios  should  be 
equal.  In  the  customary  language,  we  have  found  that  the  ratio 
of  the  sine  of  the  angle  of  incidence  to  the  sine  of  the  angle 
of  refraction  is  constant  (within  a  certain  limit  of  experimental 
error)  for  air  and  the  glass  plate,  for  the  different  angles  of 
incidence. 

It  should  be  noted  that  the  index  of  refraction  of  a  substance 
is  defined  as  the  ratio  of  the  sine  of  the  angle  of  incidence  to 
the  sine  of  the  angle  of  refraction  for  light  traveling  from  a  vacuum 
(or  air)  into  the  substance.  This  is  why  we  have  assumed  the 
direction  of  the  light  in  the  above  experiment  to  be  reversed. 

Experiment  93.  —  To  find  whether  the  ratio  of  the  real  width 
of  the  piece  of  plate  glass  to  its  apparent  width,  viewed  through  it 
perpendicularly  to  a  polished  end,  is  equal  to  its  index  of  refraction. 

Experimental  Work.  —  Paste  a  strip  of  paper  B  (Fig.  73)  on 
one  side  of  the  glass  plate  used  in  Experiment  92,  so  as  to  over- 
lie the  perpendicular  from  one  of  the 
scratches  A.  Hold  the  plate  in  one 
hand  on  a  level  with  the  eyes,  and  look 
with  both  eyes  at  the  scratch  through  the 
polished  end  CD,  along  the  line  NA 
perpendicular  to  CD\  and  at  the  same 
time  look  through  the  air  at  the  sharp 
point  of  your  pencil,  as  you  place  it  in 
apparent  coincidence  with  the  scratch. 

In  doing  this  you  will  find  it  helpful  to  move  the  pencil  forward 
until  it  is  evidently  a  little  nearer  than  the  image  of  the  scratch, 
then  back  till  it  is  a  little  farther  than  the  image,  gradually  diminish- 
ing the  distance  till  the  exact  point  is  located.  Shifting  the  head 
very  slightly  from  side  to  side  is  sometimes  helpful.  It  should  be 
possible  to  locate  the  image  of  the  scratch  within  .2  or  .3  mm. 


REFRACTION   THROUGH    A   PLATE   AND   A    PRISM       l6l 

Make  a  dot  on  the  paper  marking  the  position  of  the  image. 
Measure  the  distance  from  this  dot  to  the  surface  CD.  This  is 
the  apparent  width  of  the  glass.  Measure  its  real  width. 

Computation  and  Conclusion Divide  the  real  width  by  the 

apparent  width ;  and  compare  the  quotient  with  the  index  of 
refraction  of  the  glass  as  found  in  Experiment  92. 

It  can  be  shown  mathematically  that  the  quotient  of  the  real 
width  of  a  transparent  body  by  its  apparent  width,  when  viewed 
perpendicularly  to  'the  refracting  surface,  is  the  index  of  refraction 
of  the  substance. 

EXERCISE    50.       REFRACTION    THROUGH    A    PLATE 
.  AND   A   PRISM ;    TOTAL   REFLECTION 

References. — Adams,  272-276,  278;  Coleman,  365-369;  Car. 
&  C.,  262-263,  266-268;  Ches.  G.  &  T.,  315-318;  Hoad.  Br., 
472-473,  475-476 ;  Hoad.  EL,  520-524  ;  Mumper,  200-201,  203  ; 
Mil.  &  G.,  511-515  ;  Went-  &  H->  383-385- 

Experiment  94.  —  To  find  the  path  of  a  ray  of  light  through  a 
glass  plate  and  through  a  glass  prism  ;  and  to  observe  the  apparent 
displacement  of  objects  seen  through  each. 

Apparatus.  —  A  rectangular  piece  of  thick  plate 
glass ;  a  triangular  prism  with  flat  ends  and  wide 
faces ;  rule. 

Experimental  Work.  —  a.  Draw  a  straight  line 
AB  (Fig.  74)  a  few  centimeters  long  on  a  page 
of  your  note  book ;  stand  the  glass  plate  on  end 
obliquely  to  the  line,  and  mark  its  outline  CD  on 
the  paper.  Lay  the  rule  on  the  paper  in  front  _ 

of  the  glass ;  and,  sighting  along  its  edge  with 
one  eye,   place  the  edge  in  line  with  AB  as  seen  through  the 
glass.     Draw  a  line  on  the  paper  in  this  position,  and  letter  it  EF. 
Raise  the  plate  so  as   to  view  AB  under  it,  and  note  the  actual 
COLEMAN'S  NEW  MANUAL — n 


1 62  LIGHT 

position  of  AB  relative  to  EF.  Note  the  apparent  shifting  of  AB 
parallel  to  itself  as  the  plate  is  again  lowered.  Try  the  effect  of 
gradually  turning  the  plate  round  to  a  position  at  right  angles  to 
the  lines.  Result? 

Continue  the  lines  AB  and  EF  to  the  lines  representing  the 
surfaces  of  the  plate,  and  draw  a  straight  line  (between  the  parallel 
lines  of  CD]  joining  their  extremities.  The  broken  line  ABEF 
now  represents  the  path  of  a  ray  of  light  passing  obliquely  through 
the  plate.  Place  an  arrowhead  on  each  part  of  the  broken  line. 
Produce  FE  as  a  dotted  line  to  represent  the  apparent  position 
of  AB,  when  viewed  through  the  plate. 

b.  Stand  the  prism  on  end  on  a  page  of  your  note  book,  with 
its  rear  face  at  an  angle  of  about  45°  with  a  line  AB  (Fig.  75); 

and,  as  with  the  glass  plate,  draw  a  lir^e  FG  in 
front  of  the  prism  and  in  line  with  the  apparent 
position  of  AB  as  seen  through  the  prism. 
Draw  the  outline  of  the  base  of  the  prism,  and 
complete  the  construction,  showing  the  path  of 
a  ray  of  light  through  the  prism.  Produce  GF 
backward  as  a  dotted  line  to  represent  the 
apparent  position  of  AB.  Draw  perpendiculars 
to  CD  and  ED  at  the  points  of  entrance  and 
emergence  of  the  ray ;  letter  the  two  angles  of 
incidence  z,  the  two  angles  of  refraction  r,  and 
the  angle  of  total  deviation  d  (the  acute  angle 
between  AB  and  FG  produced). 

c.  Hold  the  glass  plate  up  before  you  with  your  pencil  behind 
it,  both  vertical,  and  the  plate  turned  obliquely  to  the  line  of  sight. 
Compare  the  apparent  position  of  the  pencil,  viewed  thus  obliquely 
through  the  glass,  with  its  real  position,  as  shown  by  the  upper  end 
of  it,  viewed  above  the  plate.     Move  the  pencil  to  a  distance  of 
a  fpot  or  more  back  of  the  plate,  and  observe  whether  the  dis- 
tance between  its  real  and  apparent  positions  changes. 

d.  Repeat  with  the  prism  in  place  of  the  plate.     In  moving  the 
pencil  away  from  the  prism,  move  it  in  such  a  direction  that  it 


REFRACTION   THROUGH   A   PLATE  AND   A   PRISM      163 

continues  visible  through  the  prism.  Compare  the  results  with 
those  obtained  with  the  plate,  and  account  for  the  difference. 

e.  Look  at  any  distant  straight  lines,  as  the*  outline  of  a  build- 
ing, through  a  common  window  pane,  and  note  their  apparent 
wavy  distortion.  Observe  their  apparent  wriggling  motion  as  the 
head  is  moved  from  side  to  side.  Explain. 

Experiment  95.  —  To  study  phenomena  due  to  total  reflection  in 
glass  and  in  water. 

Apparatus.  —  Triangular  glass  prism  with  flat  ends ;  glass  jar, 
preferably  rectangular  •  large  jar  of  water ;  beaker ;  rule ;  mop 
cloth. 

Experimental  Work.  —  a.  Lay  a  glass  prism  down  on  a  side  on 
a  printed  page.  Look  at  the  page  through  the  prism,  with  the 
eyes  at  first  directly  above  it.  Slowly  lower  the  head  so  as  to 
view  the  page  more  and  more  ob- 
liquely through  the  near  side  of  the 
prism  until  the  printing  is  no  longer 
visible.  Describe  arid  account  for 
the  appearance  of  the  lower  face  of 
the  prism  and  the  disappearance  of 
the  printing,  referring  to  a  copy 
of  Figure  76.  Remember  that  there 
is  a  thin  layer  of  air  between-  the 
prism  and  the  paper. 

b.  With  the  eyes  in  such  a  posi- 
tion  that  the  printing  is  invisible, 

test  the  reflecting  power  of  the  lower  face  of  the  prism  by  viewing 
in  it  the  image  of  your  pencil,  held  near  the  farther  face  of  the 
prism.  While  still  viewing  this  image,  slowly  raise  the  head  till 
the  printing  becomes  visible,  and  note  the  change  in  the  bright- 
ness of  the  image.  Explain. 

c.  Moisten  a  part  of  the  lower  face  of  the  prism  with  a  drop 
of  water  on  the  finger,  and  press  this  face  down  on  the  printed 
page.     Can  the  printing  be  seen  through  the  moistened  part  of 


164 


LIGHT 


the  surface  when  the  eyes  are  in  position  to  receive  total  reflec- 
tion from  the  remainder  of  it?  Find  whether  there  is  total  reflec- 
tion from  the  moistened  part  of  the  surface  at  any  angle.  With 
the  eyes  in  position  to  see  the  printing  through  the  moistened  part 
of  the  surface  but  not  through  the  remainder,  observe  the  gradual 
disappearance  of  the  printing  as  the  moisture  is  absorbed  by  the 
paper. 

In  this  experiment  water  takes  the  place  of  air  between  the 
paper  and  the  moistened  part  of  the  lower  face.  From  the 
observed  phenomena  do  you  find  the  critical  angle  at  a  glass- 
water  surface  greater  or  less  than  at  a  glass-air  surface? 

d.  Stick  a  bit  of  gummed  paper  on  the  outside  of  the  smaller 
jar  5  or  6  cm.  from  the  top.     Fill  the  jar  level  full  of  water,  and 

stand  it  near  the  edge  of  the 
table  with  the  bit  of  paper  on 
the  side  opposite  you.  Look  at 
the  paper  through  the  surface 
of  the  water,  while  gradually 
lowering  the  eyes  till  they  are 
on  a  level  with  the  surface,  and 
note  the  continuous  change  in 
the  apparent  position  of  the 
paper.  Continue  to  lower  the 
head  while  looking  upward 
through  the  side  of  the  jar  at 

the  under  side  of  the  surface  of  the  water.  Presently  an  image 
of  the  paper  will  be  seen  by  reflection  in  this  surface.  Copy 
Figure  77  and  finish  it,  showing  the  position  of  the  image  of  the 
paper  for  different  positions  of  the  eye.  Why  does  the  image  by 
reflection  not  appear  as  soon  as  the  eyes  are  too  low  to  see  it 
by  refraction  through  the  surface  of  the  water? 

e.  With  the  eyes  directed  upward  toward  the  surface  of  the 
water,  observe  in  it  the  image  of  your  pencil,  held  partly  under 
water.     What  evidence  is  there  that  this  image  is  formed  by  total 
reflection  ? 


THE  CONVEX   LENS 


I65 


EXERCISE    51.     THE   CONVEX   LENS 

References.  —  Adams,  318-326;  Coleman,  374-379;  Car.  & 
t.,  269-274  ;  Ches.  G.  &  T.,  321-329  ;  Hoad.  Br.,  477-480,  483- 
484;  Hoad.  EL,  525-528,  530-532;  Mumper,  204-206;  Mil.  & 
G.,  546-549  ;  Went.  &  H.,  386-388,  390. 

Experiment  96.  —  To  find  the  focal  length  of  a  convex  lens;  and 
to  study  the  formation  of  real  and  virtual  images  by  it. 

Apparatus.  —  Meter  rod ;  mounted  lens,  having  a  focal  length 
of  10  to  15  cm.;  two  mounted  cardboard  screens,  one  having  a 
circular  hole  about  5  cm.  in  diameter  at  the  same  height  as  the 
lens ;  mounted  candle. 

[Various  inexpensive  supports  for  lenses  are  supplied  by  dealers. 
Figure  78  shows  very  satisfactory  metal  supports  for  lens  and 
screen.  The  support  for  the  lens  should  have  a  neck,  as  shown 


FIG.  78. 


in  the  figure,  to  hold  the  lens  several  centimeters  above  the  meter 
rod.  This  is  much  more  convenient  than  to  have  the  lens  down 
on  the  rod.  Figure  79  shows  another  form  of  support,  consisting 
of  a  wooden  block  and  upright  strips  of  brass.] 

Experimental  Work.  —  a.  Place  the  lens  at  about  the  middle 
of  the  meter  rod,  and  turn  it  toward  some  distant  object,  visible 
through  an  adjacent  window.  If  it  is  not  too  cold,  open  the 
window,  to  avoid  the  unequal  refraction  of  the  glass.  Place  the 
screen  with  the  hole  close  behind  the  lens  (i.e.  on  the  side  oppo- 


1 66  LIGHT 

site  to  the  object).  Place  the  other  screen  back  of  the  first,  and 
adjust  its  distance  so  that  a  distinct  image  of  the  distant  object 
is  focused  on  it.  The  screen  with  the  hole  is  to  intercept  as 
much  of  the  light  from  other  sources  as  possible.  Note  the  effect 
of  removing  it. 

Measure  the  distance  from  the  lens  to  the  image.     (If  the  lens 

•  and  screen  are  mounted  at  the  middle  of  blocks  of  the  same 

length,  take  the  readings  of  the  meter  scale  at  corresponding  ends 

of  these  blocks,  and  subtract  one  from  the  other.)     This  distance 

is  the  focal  length /of  the  lens. 

b.  Remove  the  screen  on  which  the  image  is  focused,  and  stand 
the  other  screen  in  its  place,  so  that  the  image  will  be  in  the  air 
in  the  hole  of  this  screen.     Place  the  head  a  foot  or  two  back 
of  the  screen,  and  look  at  the  image  with  both  eyes,  focusing 
them  on  the  hole   (not  on  the  more  distant  lens).     The  screen 
serves  merely  as  an  aid  in  focusing  the  eyes  on  the  real  position 
of  the  image.     You  may  succeed  without  it,  though  this  is  difficult 
for  the  beginner.     If  not  quickly  successful  in  trying  to  view  the 
image  directly,  pass  it. 

c.  Take  the  apparatus  to  a  darkened  corner  of  the  room,  or, 
better,  to  a  room  where  all  the  shades  can  be  drawn.     Place  the 
lens  near  the  middle  of  the  rod  and  the  lighted  candle  at  one 
end.     Focus  the  image  of  the  candle  on  the  screen  to  determine 
its  position,  then  remove  the  screen  and  view  it  directly.     Observe 
the  change  in  the  size  and  position  of  the  image  (either  viewing  it 
directly  or  focusing  it  on  the  screen)  as  your  companion  slowly 
carries  the  candle  from  its  present  position  to  a  distance  of  several 
meters.     Repeat  a  number  of  times,  comparing  roughly  the  dis- 
tances through  which  the  candle  and  the  image  move.     Does  the 
position  of  the  image  change  more  or  less  rapidly  for  a  given 
motion  of  the  candle  as  the  distance  of  the  candle  becomes  large? 

Measure  the  distance  of  the  image  from  the  lens  when  the 
candle  is  at  its  greatest  distance,  and  compare  with  trie  focal 
length  of  the  lens.  What  point  would  the  image  approach  if  the 
distance  of  the  candle  were  increased  indefinitely? 


THE   CONVEX   LENS  1 67 

d.  Move  the  candle  slowly  toward  the  lens  from  a  distance  of 
about  half  a  meter,  and  follow  the  change  in  the  size  and  position 
of  the  image,  by  focusing  it  on  the  screen.     Does  it  move  more  or 
less  rapidly  than  the  object? 

Focus  the  image,  if  possible,  on  a  distant  wall  of  the  room,  and 
measure  the  distance  of  the  candle  from  the  lens.  Compare  this 
distance  with  the  focal  length.  What  would  become  of  the  image 
if  the  candle  were  moved  up  to  the  principal  focus? 

e.  Place  the  eye  close  to  the  lens  and  look  through  it  at  the 
candle,  and  observe  the  change  in  its  apparent  size  and  position 
as  you  move  it  toward  the  lens  from  a  position  beyond  the  prin- 
cipal focus.     What  appears  to  be  the  "  magnified  candle  "  is  the 
magnified  virtual  image  of  the  candle. 

/.  Standing  in  a  well-lighted  part  of  the  room,  hold  the  lens  in 
one  hand  at  a  distance  of  about  30  cm.,  and  hold  your  pencil 
close  behind  it.  Look  with  both  eyes  through  the  lens  at  the 
image  of  the  pencil,  and  compare  its  size  and  position  with  the 
part  of  the  pencil  seen  above  the  lens,  as  you  slowly  move 
the  pencil  back  from  the  lens.  Continue  the  observation  as  you 
move  the  pencil  back  and  forth  through  the  whole  distance  within 
which  the  image  remains  distinct.  If  you  have  difficulty  in  seeing 
the  image  in  its  true  position,  keep  the  eyes  steadily  on  it  as  you 
start  with  the  pencil  close  to  the  lens  and  move  it  slowly  back. 
A  slight  shifting  of  either  the  lens  or  the  pencil  from  side  to  side 
is  also  helpful.  Find  frorn1  these  observations  the  answers  to  the 
following  questions  :  — 

Is  the  distance  of  the  image  ever  greater  than  that  of  the 
object?  Is  it  always  greater?  Which  increases  more  rapidly,  the 
distance  of  the  object  or  the  distance  of  the  image? 

How  does  the  size  of  the  image  change  as  the  object  is  moved 
back  from  a  position  close  to  the  lens? 

What  is  the  greatest  distance  of  the  object  at  which  the  image 
remains  distinct?  (Measure  it  and  compare  with  the  focal  length 
of  the  lens.)  Why  is  the  image  indistinct  when  the  object  is  at 
a  greater  distance  than  this? 


1 68  LIGHT 

Discussion.  —  From  the  results  of  the  experiment,  together  with 
a  study  of  the  text,  find  answers  to  the  following  questions  :  — 

1.  What  happens  after  refraction  to  the  diverging  cone  of  light 
that  falls  upon  the  \ens/r0m  any  one  point  of  the  object,  (a)  when 
the  distance  of  the  object  is  greater  than  the  focal  length?  (b)  less 
than  the  focal  length?   (c)  equal  to  the  focal  length? 

2.  What  behavior  of  the  refracted  light  results  in  (a)  a  real 
image?   (b)  a  virtual  image? 

3.  (a)  Under  what  conditions  is  a  real  image  formed?  (b)  a 
virtual  image? 

4.  With  rule  and  compass  draw  accurate  figures  showing  the 
size  and  position  of  the  image  in  the  following  cases.     Use  the 
same  focal  length  in  all  the  figures,  and  in  all  but  the  first  an 
arrow  of  the  same  length  as  object.     The  object  cannot  be  rep- 
resented in  the  first  figure.     (Why  not?) 

Object  large  and  at  a  relatively  great  distance  (illustrating 
paragraph  a). 

Distance  of  object  greater  than  twice  the  focal  length  (illustrating 
paragraph  c). 

Distance  of  object  greater  than  the  focal  length  and  less  than 
twice  the  focal  length  (illustrating  paragraph  </). 

Distance  of  object  slightly  less  than  the  focal  length,  and 
also  when  only  a  small  fraction  of  the  focal  length  (illustrating 
paragraph/). 

EXERCISE   52.     CONVEX   AND    CONCAVE   LENSES 

References. — Adams,  319-327;  Coleman,  380,  382;  Car.  & 
C.,  271-274;  Ches.  G.  &  T.,  330;  Hoad.  Br.,  481-482;  Hoad. 
EL,  525-532;  Mumper,  206-207;  Mil.  &  G.,  550-551;  Went. 
&  H.,  386-390. 

Experiment  97.  —  To  find  the  focal  length  of  a  convex  lens  from 
its  relation  to  conjugate  focal  distances  ;  and  to  compare  the  rela 
five  size  of  image  and  object  with  their  respective  distances  from 
the  lens. 


CONVEX   AND   CONCAVE   LENSES 


169 


Apparatus.  —  Lens  of  10  to  15  cm.  focal  length;  meter  rod; 
two  mounted  screens,  one  having  a  round  hole  about  i  in.  in 
diameter,  with  cross  wires  (Fig.  79)  ;  flat  gas  jet  or  lamp. 

Experimental  Work.  — Find  the  focal  length /of  the  lens  by 
focusing  the  image  of  a  distant  object  on  a  screen,  as  in  the  pre- 
ceding exercise. 

Draw  the  window  shades,  at  least  those  near  the  apparatus,  so 
as  to  make  the  room  rather  dark.  Stand  the  screen  with  the 


FIG.  79. 


cross  wires  at  an  end  of  the  rod,  and  turn  the  gas  jet  flatwise 
toward  it.  Place  the  lens  at  a  distance  exactly  equal  to  twice  its 
focal  length  from  this  screen,  and  adjust  the  other  screen  so  that 
the  image  of  the  cross  wires  is  exactly  focused  upon  it.  The 
image  of  the  cross  wires  may  be  red,  black,  or  greenish  blue,  de- 
pending upon  the  position  of  the  screen.  Adjust  for  a  black 
image.  Let  /  denote  the  distance  from  the  lens  to  the  cross 
wires,  and  /'  from  the  lens  to  the  image.  Record  as  indicated 
below.  Measure  carefully  the  diameter  of  the  hole  contain- 
ing the  cross  wires  and  the  diameter  of  the  image.  Call  the 
first  the  length  of  the  object  /,  and  the  second  the  length  of  the 
image  /'. 

Move  the  screen  on  which  the  image  is  caught  to  the  farther 
end  of  the  rod ;  then  move  the  lens  toward  the  cross  wires  till  the 
image  is  again  distinct  on  the  screen.  Measure/,/',  and  /'. 


LIGHT 


Without  changing  the  position  of  either  screen,  move  the  lens 
away  from  the  cross  wires  till  the  image  again  falls  upon  the  other 
screen ;  and  measure  p,  /',  and  /'. 

Data  and  Computations.  —  Consult  the  text-book  for  the  deri- 
vation of  the  lens  formula  \/p  +  i//'  =  i//.  Solved  for  f,  this 
gives /=//'/(/+/').  The  average  of  the  three  values  of/ com- 
puted from  this  formula  is  the  focal  length  of  the  lens  as  found  by 
the  method  of  conjugate  foci.  Compare  this  with  the  value  ob- 
tained by  focusing  on  a  distant  object. 

Consult  the  text,  also,  for  the  geometrical  proof  that  the  true 
values  of  the  ratios  p'/p  and  ///  are  equal.  Write  all  ratios  in 
the  tabulated  record  as  quotients  expressed  decimally.  Record 
as  follows  :  — 


•ft 

•ftf 

tt 

// 

j.r  Ij. 

1'  17 

DIFFERENCE 

PER  CENT 

p 

P 

p+p> 

P  IP 

i  ft 

P'lP  ~  I'/i 

OF  DlFF. 

o/ 

/o 
o/ 

cm. 

cm. 











/o 

°/ 

/o 

Focal  length  of  lens  /  found  by  focusing  on 

a  distant  object 
Average  value  of  focal  length,  computed  from 

conjugate  focal  distances 
Percentage  of  difference  between  focal  lengths 

by  the  two  methods 
Diameter  of  circular  hole  (length  of  object)  / 


=        cm. 


=        cm. 


=        cm. 


Discussion.  —  a.  Show  from  the  formula  that/  and  /'  should 
be  equal  in  the  first  set  of  measurements. 

b.  How  do  /  and/'  of  the  second  set  of  measurements  com- 
pare with  /  and  /  respectively  of  the  third  set  ?  What  principle 
of  conjugate  foci  is  illustrated  by  these  two  pairs  of  values? 


THE  EYE 


171 


Experiment  98.  —  To  study  the  formation  of  images  by  a  con- 
cave lens. 

Apparatus.  —  Concave  lens. 

Experimental  Work.  —  a.  Try  to  focus  a  beam  of  sunlight  on 
a  sheet  of  paper  with  the  concave  lens,  as  you  do  with  a  convex 
lens.  State  and  account  for  the  result. 

b.  Hold  the  lens  up  before  a  window  (preferably  open)  at  a 
distance  of  a  foot  or  more  from  the  face,  and  look  through  it 
with  both  eyes  at  the  image  of  distant  objects.     Shift  the  lens 
slightly  from  side  to  side  to  aid  in  locating  the  image.     The  dis- 
tance of  the  image  is  the  focal  length  of  the  lens.     Estimate  this 
distance  as  closely  as  you  can. 

c.  Look  at  nearer  objects  through  the  lens,  —  as  the  window, 
the  floor,  a  page  of  your  book,  your  hand,  a  pencil,  etc.,  —  always 
with  both  eyes  and  with  the  lens  a  foot  or  more  from  the  face. 
Compare  the  relative  size  and  distance  of  object  and  image  in 
each  case.     As  the  object  approaches  the  lens,  what  change  takes 
place  in  the  size  and  position  of  its  image?     Where  is  the  image 
when  the  object  is  close  to  the  lens? 

Draw  three  diagrams  showing  the  formation  of  an  image  by  a 
concave  lens ;  the  first  with  a  large  object  at  a  relatively  great 
distance  (the  object  not  shown  in  the  figure);  the  second  with 
the  object  (represented  by  an  arrow)  at  about  twice  the  focal 
length ;  the  third  with  the  distance  of  the  object  about  one  fourth 
the  focal  length.  Take  the  same  focaHength  in  the  three  diagrams. 

EXERCISE   53.     THE   EYE 

(INVENTIVE) 

References.  —  Adams,  331-333;  Coleman,  383-386;  Car.  & 
C.,  301-302;  Hoad.  Br.,  520-521;  Hoad.  EL,  570-572;  Mum- 
per, 215  ;  Mil.  &  G.,  555  ;  Went.  &  H.,  403-404. 

Experiment  99.  —  To  study  the  structure  of  the  eye  by  means  of 
a  dissected  model. 

Apparatus.  —  A  large  anatomical  model  of  the  eye,  separable. 


1/2  LIGHT 

Suggestions.  —  Examine  the  model  in  connection  with  the 
study  of  the  text  and  any  school  physiology  on  the  subject  of  the 
eye.  Handle  the  model  only  with  clean  hands  and  as  little  as 
will  serve  the  purpose,  to  avoid  unnecessarily  soiling  it.  Make 
note  of  any  points  not  fully  understood,  and  bring  them  up  for 
discussion  in  the  recitation.  The  parts  of  the  eye,  their  appear- 
ance, shape,  relative  position,  physical  properties,  structure,  and 
function  should  all  receive  attention,  primarily  from  the  point  of 
view  of  the  eye  as  an  optical  instrument. 

Experiment  100.  —  To  examine  a  dissected  eye  of  an  ox. 
Material.  —  An  ox's  eye,  dissected  by  the  teacher. 

Suggestions.  —  If  several  pupils  are  to  study  the  same  eye,  it 
should  be  disturbed  but  little.  At  the  most,  use  the  scalpel  or 
other  dissecting  instrument  to  move  the  parts  slightly,  if  neces- 
sary to  get  a  good  view  of  them,  or  to  test  their  texture,  rigidity, 
etc.  Examine  the  specimen  closely  in  connection  with  a  study 
of  the  text  or  any  physiology. 

EXERCISE    54.    THE    SIMPLE  AND  THE    COMPOUND 
MICROSCOPE 

References.— Adams,  335-336;  Coleman,  393-395  ;  Car.&C., 
295-296;  Hoad.  Br.,  513-514;  Hoad.  EL,  562-563;  Mumper, 

206,  211  ;  Mil.  &  G.,  556-558,  560  ;  Went.  &  H.,  406,  411-412. 

• 

Apparatus.  —  Two  mounted -lenses,  preferably  of  equal  focal 
length  not  over  10  cm. ;  meter  rod;  two  small  mounted  screens 
with  printing  and  metric  scale. 

[Lenses  and  screens  mounted  as  in  Figure  78  are  preferable. 
The  screens  are  better  small —  not  over  6  by  8  cm.  Printing  in 
the  same  size  of  small  type  is  pasted  on  one  side  of  each  screen 
and  a  paper  metric  scale  5  cm.  long  at  the  left  edge  of  the  other 
side.  The  screens  should  be  held  in  their  supports  only  by  the 
pressure  of  the  springs,  so  that  they  can  be  shifted  to  right  or 
left.] 


THE  SIMPLE  AND  THE  COMPOUND    MICROSCOPE      173 

Experiment  101. —  To  find  the  magnifying  power  of  a  simple 
microscope. 

Experimental  Work.  -—  a.  Place  a  lens  at  an  end  of  the  meter 
rod,  and  adjust  one  of  the  screens  back  of  it  so  as  to  read  the 
fine  printing  with  one  eye,  placed  close  to  the  lens.  Estimate 
the  magnification. 

b.  Place  both  of  the  screens  behind  the  lens  on  the  rod,  with 
the  metric  scales  turned  toward  the  lens,  and  the  farther  screen  at 
a  distance  of  25  cm.  from  the  lens.     Adjust  the  nearer  screen  so 
that  the  scale  is  distinctly  seen  through  the  lens,  with  the  eye 
close  to  it. 

With  the  screens  remaining  at  these  distances  and  the  scales  at 
the  left  side  of  each  (invert  if  necessary),  shift  the  nearer  screen 
to  the  right  until  the  scale  is  directly  over  the  meter  rod.  Look 
at  this  scale  with  the  right  eye,  placed  close  to  the  lens,  and 
at  the  same  time  look  through  the  air  with  the  left  eye  at  the 
farther  scale.  While  looking  thus  with  both  eyes,  slip  the  farther 
scale  to  the  left  till  it  appears  to  the  left  and  close  beside  the 
image  of  the  nearer  scale.  (If  you  prefer  to  look  through  the  lens 
with  the  left  eye,  read  right  instead  of  left,  and  vice  versa,  in  the 
above  directions.)  If  you  have  difficulty  in  seeing  both  scales 
distinctly  at  the  same  time,  winking  with  one  eye  or  the  other, 
or  both,  will  help.  Note  as  accurately  as  possible  the  length  on 
the  farther  scale  that  is  equal  to  a  centimeter  on  the  magnified 
image  of  the  nearer  scale. 

This  gives  the  magnification  produced  by  the  lens  when  used  to 
the  best  advantage  as  a  simple  microscope.  For  example,  if  the 
magnified  centimeter  has  the  same  length  as  2  cm.  on  the  scale 
which  is  viewed  with  the  naked  eye  at  25  cm.  (the  least  distance 
of  distinct  vision),  the  magnification  is  2. 

c.  Compare  the  magnification,  thus  determined,  with  the  ratio 
of  the   distance  of  the  farther  screen  (25  cm.)  to  the  distance  of 
the  nearer  screen  from  the  lens.     Record  the  latter  distance  as 
well  as  the  ratio. 


1 74  LIGHT 

d.  Find  the  focal  length  of  the  lens  /  by  focusing  it  on  a  dis- 
tant object.  Compute  the  ratio  of  25  cm.  to  the  focal  length. 
This  ratio  (2$//,  the  distances  being  measured  in  centimeters)  is 
the  formula  for  computing  the  approximate  .value  of  the  magnifica- 
tion from  the  known  focal  length  (see  text). 

Oral  Discussion.  —  i.  Is  the  ratio  determined  in  c  or  in  d  more 
nearly  equal  to  the  magnification  as  determined  by  direct  com- 
parison ? 

2.    Which  should  you  expect  to  be  more  nearly  equal,  and  why? 

Experiment  102.  —  To  adjust  and  use  a  pair  of  lenses  as  a  com- 
pound microscope;  and  to  determine  the  magnification. 

Experimental  Work.  —  a.  Leave  the  lens  that  you  have  been 
using  at  the  end  of  the  rod,  to  serve  as  the  eye  lens.  Place  the 
other  lens  (the  objective)  on  the  rod  at  a  distance  of  four  or  five 
times  the  focal  length  from  the  first.  (The  two  lenses  are  of  equal 
or  nearly  equal  focal  length.)  Place  one  of  the  screens  beyond 
the  objective,  with  the  printing  turned  toward  you ;  and  adjust  its 
distance  so  that  the  printing  is  distinct  when  viewed  through  the 
two  lenses.  Probably  not  more  than  two  or  three  letters  v/ill  be 
visible,  the  field  of  view  being  very  small.  Note  the  distortion 
and  coloring  of  the  image.  These  imperfections  and  their  remedy 
are  discussed  in  the  text.  The  image  will  appear  greatly  magni- 
fied in  comparison  with  the  printing  viewed  directly  with  the 
other  eye  at  that  distance  (50  to  60  cm.  with  lenses  of  10  cm. 
focal  length)  ;  but  the  correct  comparison  is  made  with  the  print- 
ing as  it  appears  to  the  unaided  eye  at  a  distance  0/2$  cm.  The 
metric  scales  will  be  used  for  this  purpose  in  the  work  of  the  next 
paragraph. 

b.  Reverse  the  screen,  and  slip  it  to  right  or  left  till  as  much  of 
the  scale  as  possible  is  distinctly  visible  through  the  lens.  Hold 
the  other  screen  in  the  hand  25  cm.  from  the  eye  lens  and  in  such 
a  position  that  the  scale  on  it,  'viewed  directly  with  one  eye, 
appears  close  beside  the  image  of  the  farther  scale,  viewed  through 
the  lenses  with  the  other  eye.  From  a  comparison  of  the  scales, 


THE   SIMPLE   AND   THE   COMPOUND   MICROSCOPE      175 

determine  the  magnification.  For  example,  if  2  mm.  of  the  mag- 
nified scale  appear  as  long  as  9  mm.  on  the  other,  the  magni- 
fication is  9/2,  or  4.5. 

c.  Measure  the  distance  between  the  lenses  and  the  distance 
from  the  objective  to  the  screen  used  as  object. 

Let/  denote  the  latter  distance  (represented  by  AO  in  Figure 
80)  and/'  the  distance  from  the  objective  to  the  real  image  formed 


FIG.  80. 


by  it  (Oa  in  the  figure).  This  real  image  ba  is  approximately  at 
the  principal  focus  of  the  eye  lens  (really  at  a  somewhat  less  dis- 
tance from  the  eye  lens,  as  an  object  would  be  when  viewed 
through  the  eye  lens  alone)  ;  hence  the  approximate  value  of/'  is 
found  by  subtracting  the  focal  length  of  the  eye  lens  from  the  dis- 
tance between  the  lenses. 

Since  /  and  /'  are  conjugate  focal  distances,  the  magnification 
due  to  the  objective  alone  is  /'//.  The  magnification  due  to  the 
eye  lens  is  the  same  as  when  that  lens  is  used  alone,  its  approxi- 
mate value  being  25/7.  Hence  the  magnification  due  to  objective 
and  eye  lens  together  is/'//  x  2$/f.  Compute  the  magnification 
from  this  formula,  and  compare  with  the  value  found  by  direct 
observation. 

Record  data  and  computations  in  the  usual  form. 


176  LIGHT 

EXERCISE  55.    THE  ASTRONOMICAL  AND  THE  GALI- 
LEAN  TELESCOPE 

References. — Adams,  337-338;  Coleman,  396,  398;  Car.  £ 
C.,  297-298  ;  Hoad.  Br.,  515-517  ;  Hoad.  EL,  564-566  ;  Mumper, 
212,  214;  Mil.  &  G.,  559,  562;  Went.  &  H.,  413-415. 

Apparatus.  —  Convex  lens  of  long  focal  length;  two  convex 
lenses  of  unequal  short  focal  length ;  concave  lens  of  short  focal 
length;  two  mounted  screens,  one  with  a  hole  of  1.5  in.  diameter 
at  height  of  lenses  ;  meter  rod ;  metric  rule. 

[The  lenses  commonly  supplied  for  laboratory  work  have  a 
focal  length  of  10  to  15  cm.  If  these  are  used  as  eye  lenses  in 
this  experiment,  the  objective  should  have  a  focal  length  of  40  cm. 
or  more ;  but  a  diameter  of  4  cm.  is  quite  sufficient.  Dealers 
will  supply  such  lenses,  made  to  order,  at  a  moderate  price. 
Lenses  of  15  to  16  cm.  focal  length  can  be  used  as  objectives 
with  lenses  of  3  to  8  cm.  focal  length  for  eye  lenses.  The  latter 

can  be  obtained,  mounted  in  various  ways,  as  simple  microscopes.] 

0 

Experiment  103. —  To  adjust  and  use  a  pair  of  lenses  as  an 
astronomical  telescope  ;  and  to  determine  the  magnification. 

Experimental  Work.  —  a.  Find  the  focal  lengths  of  the  three 
convex  lenses  by  focusing  on  a  distant  object.  The  screen  with 
the  hole,  placed  just  back  of  the  lens  to  cut  off  diffused  light, 
will  probably  not  be  sufficient  to  make  the  image  visible  with  the 
lens  of  long  focal  length,  as  the  image  is  large  and  correspond- 
ingly faint.  Lower  the  window  shade  nearly  to  the  level  of  the 
table,  and  stand  before  the  window  so  as  to  cut  off  light  from  the 
side  as  much  as  possible.  Let/  denote  the  greatest  focal  length, 
/  the  next,  and  /  the  shortest.  The  lenses  will  be  referred  to 
as  lens/j,  lens/,  and  lens/. 

b.  Place  lens  /  as  eye  lens  at  an  end  of  the  meter  rod,  and 
lens/  as  objective  at  a  distance  from  the  first,  approximately  equal 
to  the  sum  of  their  focal  lengths.  Turn  the  telescope  thus  formed 


ASTRONOMICAL   AND    GALILEAN  TELESCOPE 


177 


toward  a  distant  object ;  and,  with  the  eye  close  to  the  lens,  adjust 
the  objective  till  the  image  is  distinct.  The  window  should  be 
raised  if  the  weather  will  permit.  Note  the  border  of  color  round 
the  edges  of  objects.  Is  the  color  stronger  when  you  look  through 
the  centers  of  the  lenses  or  through  their  marginal  portions?  This 
defect  and  its  remedy  is  discussed  in  the  text  under  chromatic 
aberration  and  achromatic  lenses. 

c.   Turn  the  telescope  toward  a  distant  chimney,  tower,  water 
tank,  or  other  regular  object  of  moderate  size.     A  window  will 


J. 


FIG.  81. 

serve,  or  a  letter  of  a  large  sign ;  but  an  isolated  object  having  the 
sky  as  a  background  is  much  the  best.  Support  the  meter  rod 
upon  books  or  blocks,  or  with  a  stand  and  clamp,  so  that  it 
can  be  pointed  steadily  toward  the  object.  While  looking  at  the 
object  directly  with  one  eye  and  through  the  telescope  with 
the  other,  turn  the  telescope  so  that  the  image  directly  overlies 
the  object,  and  estimate  the  magnification. 

d.  Measure   the   distance   between   the   lenses.     This   is   the 
length  /  of  the  telescope. 

e.  Repeat  the  above  work  with  the  same  objective  and  lens  f2 
as  the  eye  lens ;  and  again  with  lens^  as  the  objective  and  lensy^ 
as  the  eye  lens. 

Data  and  Computations.  —  Compare  the  estimated  magnification 
in  each  case  with  the  ratio  of  the  focal  length  of  the  objective  to 
the  focal  length  of  the  eye  lens.     Compare  also  the  length  of 
COLEMAN'S  NEW  MANUAL — 12 


LIGHT 


the  telescope  with  the  sum  of  the  focal  lengths  of  objective  and 
eye  lens.     Record  as  follows  :  — 

Focal  length/  =      cm.,  /2  =      cm.,   /3  = 


cm. 


ESTIMATED 
MAGNIFICATION 

COMPUTED 
MAGNIFICATION 

DIFFERENCE 

I 

SUM  OF 
FOCAL  LENGTHS 

DIFFERENCE 



/1//3=  — 



cm. 

/!+/«=- 





/!//*=  — 



cm. 

/1+/2-- 

• 



/2//3  =  



/-      .      r   



- 

Discussion. —  i.  Discuss  the  first  and  second  combinations  of 
lenses  as  an  illustration  of  the  effect  of  the  focal  length  of  the  eye 
lens  on  the  magnification. 

2.  Discuss  the  first  and  third  combinations  as  an  illustration  of 
the  effect  of  the  focal  length  of  the  objective  on  the  magnification. 

3.  Discuss  the  relation  between  the  lengths  of  the  telescopes 
and  the  sum  of  the  focal  lengths  of  the  objective  and  eye  lens. 

4.  Copy  Figure  81  and  answer  the  following  questions  :  — 

a.  Which  rays  come  from  a  point  at  the  top  of  the  object,  and 
which  from  a  point  at  the  bottom? 

b.  What  (in  the  figure)   is  the  focal  length  of  the  objective? 
of  the  eye  lens? 

c.  What  is   the  visual   angle  with  the  naked  eye  ?  with  the 
telescope  ? 

</.   What  ratio  (of  lengths)  measures  the  magnification? 

Experiment  104.  —  To  adjust  and  use  a  convex  and  a  concave 
lens,  as  a  Galilean  telescope  ;  and  to  determine  the  magnification. 

Experimental  Work.  —  a.  To  find  the  focal  length  of  the  con- 
cave lens,  hold  it  about  a  foot  from  the  face,  look  through  it  with 
both  eyes  at  the  image  of  a  distant  building,  and  measure  with 
the  rule  the  distance  between  the  image  and  the  lens.  In  doing 
this,  look  at  the  farther  end  of  the  rule  directly  (not  through  the 
lens),  and  extend  it  just  to  the  image.  (The  method  is  similar  to 


THE   SPECTRUM;    COLOR 


179 


that  of  finding  the  apparent  width  of  a  glass  plate  or  the  apparent 
depth  of  water  in  a  vessel.) 

b.    Place  the  concave  lens  at  the  end  of  the  t meter  rod.     This 
is  the  eye  lens.     Use  the  lens  of  long  focal  length  /x  as  the  ob- 
r 


H  — 


FIG.  82. 

jective,  and  place  it  at  the  greatest  distance  from  the  eye  lens 
that  will  give  a  distinct  image  of  a  distant  object.  Estimate  the 
magnification  and  measure  the  distance  between  the  lenses. 

Discussion.  —  i .  Compare  the  length  of  the  telescope  with 
the  difference  between  the  focal  lengths  of  the  lenses. 

2.  Compare  the  estimated  magnification  with  the  ratio  of  the 
focal  length- of  the  objective  to  that  of  the  eye  lens. 

3.  Copy  Figure  82  and  answer  the  questions  under  4  of  the 
discussion  at  the  end  of  the  preceding  experiment. 

EXERCISE   56.     THE   SPECTRUM;  COLOR 

References.  —  Adams,  277-280,  286-291,  299-300;  Coleman, 
401,  403-404,  407-408,  410,  419;  Car.  &  C.,  277-278,  287-289, 
291-293;  Ches.  G.  &  T.,  33J-332,  339,  341-352;  Hoad.  Br., 
486-487,  494-496,  498-499,  508-509  ;  Hoad.  EL,  534~536>  543- 
546,  556-557;  Mumper,  209,  217-221;  Mil.  &  G.,  565-574; 
Went.  &  H.,  392-394,  417-418,  422-425. 

Experiment  105.  —  To  determine  by  analysis  with  a  prism  the 
elementary  or  prismatic  colors  of  sunlight,  of  light  transmitted 
through  colored  glass,  and  of  light  reflected  from  colored  surfaces. 


1 80  LIGHT 

Apparatus.  —  Prism  of  flint  glass ;  square  of  black  cardboard 
(Fig.  83)  with  a  slit  i  mm.  by  2  cm.  and  a  slit  i  cm.  by  2  cm.; 
pieces  of  colored  glass  3  to  5  cm.  square  ; 
strips  of  colored  paper  i  mm.  wide  and  2  cm. 
long,  pasted  on  black  cardboard. 

[A  prism  of  crown  glass  will  serve,  but  . 
flint  glass  gives  nearly  twice  the  dispersion, 
which  is  an  advantage.  Pieces  of  cardboard 
10  or  12  cm.  square  serve  for  the  slits  and 
the  strips  of  colored  paper.  For  these  strips 
use  white  and  several  of  the  spectrum  colors  ; 
and  arrange  them  on  the  card  so  that  their  spectra  can  be  easily 
distinguished  from  one  another.  The  squares  of  colored  glass 
should  include  ruby,  yellow,  and  blue.  The  ruby  is  a  fine 
example  of  a  nearly  pure  spectrum  color.  The  yellow  and  blue 
should  be  selected  to  give  bright  green  by  transmission  through 
both.] 

Experimental  Work.  —  a.  Stand  facing  a  window,  and  hold  the 
cardboard  with  the  slits  out  nearly  at  arm's  length,  with  the  slits 
horizontal  and  strongly  illuminated  by  sunlight  (having  the  sky  for 
a  background).  Look  at  the  narrow  slit  through  the  prism,  held 
close  to  the  eye  with  its  long  edges 
horizontal  and  its  faces  turned,  as 
shown  in  Figure  84.  Looking 
obliquely  down  at  an  angle  of 
about  35°  to  the  direction  of  the 


FIG.  84. 


slit,  you  will  see  the  overlapping 
colored  images  of  it  which  together  constitute  the  spectrum  of 
sunlight.  Copy  Figure  84  on  a  large  scale,  and  mark  by  the 
initial  letters  R,  O,  .Y,  etc.,  the  colors  of  the  spectrum  in  the 
observed  order.  What  color  is  refracted  most?  what  least? 

b.  Look  at  the  wide  slit  in  the  same  way.  Record  the  colors 
in  their  observed  order  in  a  figure  similar  to  Figure  84,  but  with 
a  wide  beam  of  light  represented  instead  of  a  ray.  The  figure 


THE   SPECTRUM;    COLOR 


181 


should  account  for  the  fact  that  the  central  portion  of  the  slit 
appears  white.  Explain. 

c.  Cover  one  end  of  the  narrow  slit  with  the  blue  glass,  and 
view  the  slit  with  the  prism,  as  before.  You  now  observe  side  by 
side  the  complete  spectrum  and  the  spectrum  of  the  light  that  is 
transmitted  through  the  blue  glass.  What  colors  besides  spectrum 
blue  are  transmitted  by  the  glass?  The  colors  not  transmitted 
are  absorbed.  Record  as  shown  below,  designating  the  colors  by 
initials. 

Make  a  similar  analysis  of  the  light  transmitted  by  the  yellow 
glass,  by  the  blue  and  yellow  together,  and  by  the  other  pieces 
provided. 


COLOR  OF  GLASS 

COLORS  TRANSMITTED 

COLORS  ABSORBED 

Blue 

Yellow 

Blue  and  yellow 

Red 

• 

Etc. 

d.  Look  through  the  blue  and  yellow  pieces  of  glass  placed 
together  (not  using  the  prism),  and  note  the  color.     Explain. 

e.  Hold  the  colored  strips  on  the  cardboard  in  a  strong  light 
(direct  sunlight,  if  possible),  and  analyze  with  the  prism  the  light 
reflected  by  them.     Record  in  tabular  form,  as  in  paragraph  c, 
heading  the  first  column  "color  of  the  strip,"  the  second  "  colors 
reflected,"  and  the  third  "  colors  absorbed."     Colors  that  appear 
very  faint  in  the  spectrum  are  to  be  recorded  as  absorbed. 

Experiment  106.  —  To  determine  the  color  resulting  from  the 
synthesis  (union)  of  various  colored  lights;  and  to  distinguish 
complementary  colors. 

Apparatus.  —  Several   pieces  of  black  cardboard  on  each  of 


182 


LIGHT 


which  are  pasted  two  squares  of  colored  paper  (Fig.  85) ;  piece 

of  window  glass  about  6  by  10  cm. 

[On  pieces  of  black  cardboard  about  8  by  12  cm.,  paste  colored 

papers  4  or  5  cm.  square,  two  on  each  card,  close  together. 
Some  of  these  pairs  of  colors  are  to  be 
complementary,  others  not.  Any  of  the 
following  are  good  :  blue  and  yellow,  red 
and  bluish  green,  green  and  purple,  violet 
and  yellowish  green,  red  and  yellow,  green 
and  violet,  violet  and  red,  orange  and 
green.] 


Experimental  Work.  —  Stand  the  piece 
of  window  glass  between  the  yellow  and 
blue  squares  on  one  of  the  cards,  with 
the  yellow  color  toward  you,  as  shown  in 
Figure  85.  Look  through  the  glass  at 
Superposed  on  it  will  be  an  image  of  the 


FIG.  85. 
the   blue    square. 


yellow  square,  due  to  partial  reflection  from  the  window  glass ; 
and  the  blue  paper  will  appear  to  be  of  the  color  it  would  have  if 
all  the  light  that  enters  the  eye  from  its  direction  actually  came 
from  it.  Inclining  the  glass  forward  increases  the  amount  of  re- 
flected yellow  light  and  decreases  the  amount  of  transmitted  blue 
light,  causing  the  appearance  of  the  blue  paper  to  change  from 
blue  through  white  or  light  gray  to  yellow.  Inclining  the  glass 
backward  produces  the  opposite  effect.  Observe  the  nearest 
approach  to  white  that  can  be  obtained  in  this  way. 

Repeat  the  experiment  with  the  red  and  yellow  papers.  (It  is 
immaterial  in  any  case  which  paper  is  in  front.)  An  intermediate 
white  or  gray  is  impossible  in  this  case.  What  color  is  produced 
instead  ? 

Try  in  the  same  way  all  the  pairs  of  colors  provided.  Name  in 
one  group  all  those  pairs  of  colors  which,  like  the  blue  and  yellow, 
give  white  or  gray.  All  such  pairs  are  complementary  colors. 
Record  the  component  and  resultant  colors  in  tabular  form. 


THE   SPECTRUM;     COLOR 


183 


PURPLE 


Discussion.—  i.  Compare  all  results  with  the  arrangement  of 
colors  shown  in  Figure  86,  and  state  the  results  in  general  terms 
with  reference  to  this  arrangement. 

2.  How  is  it  possible  that  the  yel- 
low and  blue  pieces  of  glass  together 
transmit  green,  while  the  light  from 
the  yellow  and  blue  papers  gives 
white  when  combined  ? 

Experiment  107. —  To  study  the 
production  of  color  by  interference. 

Apparatus.  —  Two  pieces  of  thick 
plate  glass ;  small  iron  clamp ;  soap- 
bubble  solution  in  a  jar;  wire  loop 
with  handle. 

Experimental  Work.  —  a.  Clamp  the  two  pieces  of  glass  firmly 
together,  being  careful  to  have  the  surfaces  that  are  in  contact 
thoroughly  clean.  Hold  them  in  a  strong  light,  and  look  at  them 
from  the  illuminated  side.  Observe  the  curved  bands  of  spectrum 
colors  which  surround  the  spot  where  the  clamp  is  applied.  Ac- 
count for  them  after  consulting  the  text. 

How  do  these  bands  of  colors  change  as  you  apply  additional 
pressure  at  the  edges  of  the  plates  with  the  fingers?  How  do 
they  change  as  you  turn  the  plates  about  and  view  them  at  dif- 
ferent angles  ?  Explain. 

b.  Cover  the  wire  loop  with  a  film  of  the  soap  solution,  and 
hold  it  in  a  strong  light,  with  the  film  vertical.  Note  the  gradual 
appearance  of  bands  of  color  in  the  upper  side  of  the  film.  These 
interference  colors  are  due  to  the  gradual  thinning  of  the  upper 
part  of  the  film  under  the  action  of  gravity.  Describe. 


X.    MAGNETISM 

EXERCISE    57.     MAGNETS    AND    MAGNETIC    ACTION 

References.  — Adams,  436-443,  449-451;  Coleman,  420-428; 
Car.  &  C.,  358-369;  Ches.  G.  &  T.,  354~359 ;  Hoad.  Br.,  291- 
298,  307;  Hoad.  EL,  326-336,  345-346;  Mumper,  222-228; 
Jackson,  68-83  ;  Mil.  &  G.,  305-311;  Went.  &  H.,  240-243, 
245-246. 

Apparatus — Bar  magnet;  magnetic  needle  on  stand  (Fig.  87); 
coarse  iron  filings  or  very  small  tacks  in  a  box  longer  than  the 

magnet ;   small  .pieces 
•_MAGNETIC__    of  various  substances. 

MERIDIAN 

as  iron,  steel,  brass, 
copper,  lead,  glass, 
paper,  etc. ;  pieces  8 
or  10  cm.  square  of 
cardboard,  glass,  thin 

wood,  sheet  iron  (or  tin),  zinc,  lead,  and  brass ;  rods  of  soft 
iron,  steel  (knitting  needle),  and  brass  or  wood  of  equal  length 
(15  to  20  cm.). 

Experiment  108.  —  To  determine  the  distribution  of  attracting 
power  in  a  magnet,  the  polarity  of  a  magnet,  and  the  law  of 
magnetic  action. 

Experimental  Work.  —  a.  Lay  the  magnet  in  the  box  of  iron 
filings,  so  that  its  whole  length  comes  in  contact  with  the  filings. 
Lift  the  magnet  and  observe  the  distribution  of  the  filings  that 
cling  to  it.  Draw  a  sketch  to  illustrate.  The  regions  where  the 
power  of  attraction  is  greatest  are  called  poles.  Is  there  any 
evidence  of  attraction  at  the  center?  Remove  the  filings  by 
wiping  them  toward  the  middle  of  the  magnet. 

184 


MAGNETS   AND   MAGNETIC  ACTION  185 

b.  Test  the  attracting  power  of  the  magnetic  needle  (Fig.  87) 
in  the  same  way.     (Do  not  let  it  come  in  contact  with  the  bar 
magnet.)     The  needle  is  a  magnet  adapted  in  its  form  to  special 
uses.     Replace  it  on  its  stand. 

c.  Remove  all  magnetic  substances  to  a  distance  not  less  than 
a  meter  from  the  magnetic  needle,  and  observe  its  behavior  when 
disturbed   and   free   to   turn   on   its   support.      Does   it    always 
come  to  rest  with  the  same  end  pointing  in  the  same  direction? 
The  end  that  points  north  in  the  position  of  equilibrium  is  called 
the    north  pole.     Note   its   color  (commonly  blue),  which  serves 
to  distinguish  it  from  the  south  pole. 

The  bar  magnet,  if  supported  so  as  to  be  free  to  turn  in  a 
horizontal  plane,  would  behave  like  the  needle.1  The  end  that 
would  point  north  is  marked  N.  The  south  pole  is  sometimes 
marked  S,  sometimes  left  unmarked. 

d.  Observe  the  effect  of  bringing  each  of  the  poles  of  the  bar 
magnet  near  each  of  the  poles  of  the  magnetic  needle.     What 
action  is  observed  between   like   poles?   between   unlike   poles? 
Remember  that  the  action  between  two  bodies  is  always  mutual 
(Newton's  third  law).     Is  there  any  evidence  of  action  on  the  bar 
magnet?     Why  or  why  not?     If  not,  can  you  suggest  any  means 
by  which  it  might  be  detected? 

e.  Note  roughly  the  rapidity  of  vibration  of  the  magnetic  needle 
when  removed  from  all  magnetic  substances  and  disturbed  from 
the    position   of  equilibrium.     Note    the   change  in  the  rate  of 
vibration   as   a   pole    of  the   bar   magnet  is   slowly  brought   up 
toward  the  unlike  pole  of  the  needle.     The  increased  rate  indicates 
increased  magnetic  force.     It  can  be  shown  mathematically  that 
the   magnetic   force    acting   on  a  needle  is  proportional   to   the 
square  of  its   rate  of  vibration.     Thus,  if  the  rate  increases  to 
twice  its  original  value,  we  know  that  the  magnetic  force  is  four 

1  It  will  not  serve  in  testing  this  to  suspend  the  magnet  by  a  thread,  for  the 
tension  on  the  thread  causes  it  to  untwist  with  a  force  that  is  commonly  greater 
than  the  magnetic  force  that  tends  to  set  the  magnet  north  and  south.  An  untwisted 
fiber  should  be  used  for  the  suspension. 


!86  MAGNETISM 

times  as  great  as  at  first.  The  more  or  less  rapid  vibration  of 
the  magnetic  needle  often  serves  to  indicate  roughly  the  relative 
magnitude  of  magnetic  forces.  It  is  unnecessary  in  elementary 
physics  to  measure  them. 

What  do  your  observations  indicate  concerning  the  effect  of 
distance  from  a  magnet  on  the  magnetic  force  exerted  by  it. 

Experiment  109. —  To  distinguish  magnetic  and  nonmagnetic 
substances  ;  and  to  determine  which  of  these  act  as  magnetic  screens. 

Experimental  Work.  —  a.  Find  which  of  the  small  pieces  of 
various  substances  provided  are  attracted  by  a  magnet,  and  which 
are  not.  Classify  the  former  as  magnetic  and  the  latter  as  non- 
magnetic. 

b.  Put  a  small  quantity  of  iron  filings  (or  tacks)  on  the  card- 
board, and  move  a  pole  of  the  magnet  about  against  the  under 
side  of  the  cardboard  beneath  the  filings.     What  evidence  is  there 
of  magnetic  action  through  the   cardboard  ?      Repeat  with  the 
piece  of  sheet  iron  in  place  of  the  cardboard,  and  try  all  the  sub- 
stances provided  in  the  same  Tjay.     Classify  them  in  two  groups 
according  as  they  do  or  do  not  act  as  a  screen  to  cut  off  magnetic 
action.     What  relation  do  you  find  between  this  classification  and 
that  of  magnetic  and  nonmagnetic  substances  ? 

Gather  up  with  the  magnet  any  scattered  filings. 

c.  Hold  a  pole  of  the  bar  magnet  about  i  cm.  from*  the  unlike 
pole  of  the  magnetic  needle,  and  note  the  rate  of  vibration.     Slip 
the  piece  of  sheet  iron  between,  and  observe  the  effect  on  the  rate 
of  vibration.     Conclusion  ?    Try  the  other  substances  in  the  same 
way. 

Experiment  no.  —  To  study  phenomena  of  magnetic  induction. 

Experimental  Work.  —  a.  Find  whether  the  soft  iron  rod  at- 
tracts iron  filings.  Try  again  with  an  end  of  the  magnet  against 
the  upper  end  of  the  rod.  What  happens  to  the  load  of  filings  on 
the  end  of  the  rod  when  the  magnet  is  removed  from  the  other 
end  ?  What  does  this  indicate  concerning  the  magnetic  condition 
of  the  rod  ? 


MAGNETS  AND   MAGNETIC  ACTION  187 

b.  With  an  end  of  the  bar  magnet  against  an  end  of  the  soft 
iron  rod,  test  the  polarity  of  the  other  end  of  the  rod  by  bringing 
it  up  to  the  magnetic  needle.     Is  this  pole  like  or  unlike  the  pole 
of  the  magnet  which  is  in  contact  with  the  other  end  of  the  rod  ? 
With  the  rod  still  in  place,  reverse  the  magnet,  bringing  its  other 
pole  in  contact  with  the  rod,  and  note  the  effect  on  the  needle. 

The  iron  rod  is  itself  a  magnet  while  in  contact  with  the  bar 
magnet,  and  has  two  unlike  poles.  You  have  tested  one  of  these 
poles,  and  hence  by  inference  know  the  other.  Is  the  pole  of  the 
rod  at  the  end  touched  by  the  magnet  like  or  unlike  that  with 
which  it  is  touched  ?  Draw  a  figure  showing  the  arrangement  of 
poles  in  the  magnet  and  the  rod,  when  they  are  placed  end 
to  end. 

c.  Repeat  the  work  of  paragraph  a  with  the  steel  rod.     Do  you 
find  it  already  magnetized  ?     If  so,  how  do  you  account  for  this 
condition  ?     Determine  its  polarity  by  testing  with  the  magnetic 
needle.     Find  whether  the  polarity  of  one  end  of  it  is  reversed  by 
merely  changing  the  pole  of  the  magnet  with  which  its  other  end 
is  touched.     If  not,  find  whether  you  can  reverse  its  polarity  by 
repeatedly  rubbing  it  from  the  center  to  one  end  with  one  pole  of 
the  magnet,  and  from  the  center  to  the  other  end  with  the  other 
pole.     Are  the  poles  of  the  rod  like  or  unlike  the  poles  of  the 
magnet  that  were  applied  to  produce  them  ? 

d.  Test  the  brass  (or  wooden)  rod  as  you  did  the  iron  rod  in  a 
and  b.     In  repeating  £,  hold  a  pole  of  the  magnet  so  that  the 
distance  between  it  and  the  needle  is  a  little  greater  than  the 
length  of  the  rod,  and  observe  whether  interposing  and  removing 
the  brass  rod  between  them  has  any  effect  on  the  needle.     Try 
the  same  with  the  iron  rod. 

Does  a  nonmagnetic  substance  in  the  form  of  a  rod  affect  mag- 
netic action  ?  Does  it  in  the  form  of  a  sheet  (Exp.  109,  b}  ? 
Compare  the  effects  of  a  magnetic  substance  in  the  two  forms. 
In  this  connection  make  a  further  test  of  the  sheet  iron  by  hold- 
ing an  end  of  the  magnet  against  its  center,  while  touching  its  edge 
to  iron  filings. 


!88  MAGNETISM 

EXERCISE   58.     MAGNETIC   FIELDS 

References.— Adams,  452-455  ;  Coleman,  431-432  ;  Gar.  &  C., 
374-377;  Ches.  G.  &T.,  363-367;  Hoad.  Br.,  299-300;  Hoad. 
EL,  334-337;  Mumper,  230;  Jackson,  84-90;  Mil.  &  G.,  312- 
314;  Went.  &  H.,  249-251. 

Apparatus.  —  Two  bar  magnets;  small  compass;  board  about 

10  by  15  in.  with  parallel 
grooves  about  2  in.  apart, 
in  the  direction  of  the 
length  (Fig.  88)  ;  one  or 
more  pieces  of  thick  card- 
board 9  by  ii  in. ;  fine 
iron  filings  in  pepper  box 

r  IG.  oo. 

or  other   sifter ;    with   or 

without  blue-print  paper  and  rubber  bands  to  fasten  it  to  the 
cardboard. 

Experiment  in.  —  To  determine  the  shape  and  direction  of  the 
lines  of  force  in  the  magnetic  field  about  a  bar  magnet. 

Experimental  Work.  —  Without  Blue-print  Paper.  Place  a  mag- 
net in  one  of  the  grooves  of  the  board,  and  note  the  position  of 
its  north  and  south  poles.  Lay  the  cardboard  over  the  magnet, 
and  sprinkle  iron  filings  thinly  and  evenly  over  it  from  the  height 
of  about  a  foot.  Gently  tap  the  cardboard  at  different  points  with 
the  finger  (not  the  finger  nail),  while  holding  it  in  place.  The 
slight  jarring  helps  to  overcome  friction,  and  enables  the  filings  to 
arrange  themselves  in  lines  under  the  action  of  the  magnet. 

Place  the  compass  at  different  points  about  the  magnet,  and 
compare  the  direction  of  the  needle  in  each  position  with  the 
direction  of  the  lines  of  filings  at  that  place.  The  lines  of  filings 
are  more  or  less  irregular  and  broken  ;  the  magnetic  lines  of  force 
which  they  imperfectly  sketch  are  really  smooth,  continuous  curves. 
Draw  a  diagram  on  a  reduced  scale,  representing  the  magnet  and 
several  lines  of  force  about  it,  as  indicated  by  the  lines  of  filings. 


MAGNETIC   FIELDS  189 

Mark  the  poles  of  the  magnet  N  and  S.  Be  careful  to  represent 
the  position  and  curvature  of  the  lines  of  force,  as  correctly  as 
possible,  by  regular,  unbroken  lines.  Place  an  arrowhead  on  each 
line,  indicating  the  direction  along  the  line  in  which  the  north  pole 
of  the  compass  needle  points. 

With  Blue-print  Paper.  —  Fasten  a  sheet  of  the  blue- print 
paper,  prepared  side  up,  to  the  cardboard  by  means  of  rubber 
bands,  and  proceed  as  above,  sprinkling  the  filings  on  the  blue- 
print paper  and  omitting  the  pencil  sketch.  Keep  unused  blue- 
print paper  in  the  dark.  Mark  the  positions  of  the  north  and 
south  poles  of  the  magnet  on  the  paper,  and  place  arrowheads 
here  and  there,  indicating  the  direction  in  which  the  north  pole 
of  the  needle  points. 

Lift  the  cardboard  vertically  from  the  magnet,  and  place  it  in 
a  strong  light  (direct  sunlight,  if  possible)  for  a  few  minutes. 


A        .  B  CD 

FIG.  89. 

When  the  uncovered  parts  of  the  paper  have  turned  dark,  return 
the  filings  to  the  box  and  wash  the  paper  immediately  by  moving 
it  about  in  clean  water,  or  letting  water  run  over  it  from  the  faucet 
for  a  few  minutes.  Spread  it  out  on  a  flat  surface  to  dry,  and 
when  dry,  fasten  it  in  your  note  book.  If  left  in  the  laboratory  till 
the  following  day  to  dry,  write  your  name  on  it  for  identification. 

Experiment  112. —  To  determine  the  shape  and  direction  of  the 
lines  of  force  between  and  about  two  bar  magnets  in  different  rela- 
tive positions. 

Experimental  Work.  —  Proceed  as  above,  either  with  or  with- 
out blue-print  paper,  to  study  and  make  a  record  of  the  magnetic 
fields  between  and  about  two  bar  magnets  in  the  different  positions 
shown  in  Figure  89.  For  the  positions  shown  in  A  and  B,  place 
the  magnets  about  4  cm.  apart  in  the  same  groove  of  the  board, 


190  MAGNETISM 

and  determine  the  lines  of  force  between  and  about  their  adjacent 
ends.  For  the  arrangements  shown  in  C  and  D,  determine  the 
lines  of  force  between  and  all  round  the  magnets.  The  last  one 
or  two  cases  may  be  omitted  if  one  laboratory  period  does  not 
give  time  enough  for  all  of  them.  Mark  the  poles  of  the  magnets 
in  the  figure  or  blue  print,  and  place  arrowheads  on  the  lines,  as 
in  the  preceding  experiment. 

Be  careful  to  gather  up  all  iron  filings  and  return  them  to  the 
sifter. 

Discussion.  —  The  following  questions  are  to  be  answered  from 
a  study  of  the  diagrams  or  blue  prints  you  have  made  :  — 

1.  Do  the  lines  of  force  converge  to  a  common  point  at  or  near 
the  end  of  a  magnet,  or  to  different  parts  of  a  small  area  near  the 
end? 

2.  Do  any  lines  of  force  cross  each  other?     What  reasons  have 
you  for  thinking  that  they  can  or  cannot  cross  in  any  case  ? 

3.  Do  lines  offeree  extend  between  like  poles  or  unlike  poles, 
or  both?     What  reasons  have  you  for  thinking  that  they  can  or 
cannot  extend  between  like  poles  in  any  case  ? 


XI.     ELECTRICITY 

EXERCISE   59.     THE   SIMPLE  VOLTAIC   CELL 

References. —r- Adams,  456-463  ;  Coleman,  441-447,  453  ;  Car. 
&  C.,  428-431,  433-435;  Ches.  G.  &  T.,  376-379;  Hoad.  Br., 
346-350;  Hoad.  EL,  387-39!;  Mumper,  251-253,  257;  Jack- 
son, 30-37,  51-52;  Mil.  &  G.,  35I~352>  375~376;  Went.  &  H., 

271-274. 

Apparatus.  —  Tumbler  of  dilute  sulphuric  acid  (about  i  part  by 
volume  of  concentrated  acid  to  20  parts  of  water)  ;  copper  strip  ; 
an  amalgamated  and  an  unamalgamated  zinc  plate,  rod,  or  strip; 
copper  wire ;  double  connector  (if  necessary)  ; 
magnetic  needle  (Fig.  87) ;  glass  tray  or 
empty  tumbler. 

[The  tumbler  battery  shown  in  Figure  90 
is  most  convenient  for  this  exercise  ;  but  a 
wooden  block  with  slots  to  support  the  plates 
will  serve.  The  wires  may  be  soldered  or 
clamped  to  the  plates ;  but  soldering  will 
not  hold  in  contact  with  an  amalgamated 
surface  of  zinc.  A  photographer's  developing 
tray  of  glass  is  very  satisfactory  for  holding  the  plates  when  not  in 
use.  It  should  be  large  enough  to  hold  the  tumbler  battery,  also.] 

Experiment  113.  —  To  study  the  action  of  a  simple  voltaic  cell ; 
and  to  test  the  presence  of  an  electric  current  by  its  action  on  a 
magnetic  needle. 

Experimental  Work.  —  a.  Keep  the  zinc  and  copper  plates, 
when  not  in  use,  in  the  glass  tray  or  empty  tumbler  provided  for 
the  purpose ;  and  keep  the  amalgamated  zinc  (the  one  of  lighter 

191 


I Q2 


ELECTRICITY 


color)  from  contact  with  the  other  plates,  to  avoid  any  amalgama- 
tion of  their  surfaces.  If  the  glass  tray  is  large  enough,  stand  the 
tumbler  of  acid  on  it.  Avoid  getting  any  of  the  acid  on  the  table, 
the  clothing,  or  the  fingers. 

Place  the  unamalgamated  zinc  plate  (the  darker  one)  in  the 
tumbler  of  acid,  and  note  the  size  and  abundance  of  the  bubbles  that 
form  on  its  surface.  What  becomes  of  them  ?  They  are  bubbles 
of  hydrogen  (a  constituent  of  the  acid)  which  has  been  displaced 
by  zinc,  forming  zinc  sulphate.  The  zinc  sulphate  (a  white  solid) 
remains  dissolved  in  the  liquid,  forming  a  colorless  solution. 
Remove  the  zinc,  and  observe  whether  it  has  the  appearance  of 
having  been  partly  consumed  through  previous  use.  Place  it  in 
the  tray  or  empty  tumbler. 

b.  Place  the  strip  of  copper  in  the  acid,  and  observe  whether 
any  hydrogen  bubbles  form  on  its  surface.     Remove  the  copper, 
and  observe  whether  it  has  been  partly  consumed  through  pre- 
vious use. 

When  sulphuric  acid  acts  on  copper,  copper  sulphate  is  formed. 
This  is  a  blue  solid,  which  would  remain  dissolved  in  the  liquid 
and  would  color  it  a  greenish  blue.  Do  you  find  the  liquid  thus 
colored?  What  conclusion  do  you  draw  from  these  observations? 

c.  Support  the  copper  and  the  unamalgamated  zinc  plates  in 
the  acid  by  means  of  the  clamps  (or  other  device),  and  connect 
the  copper  wire  with  either  of  them,  leaving  its  other  end  free. 
Do  bubbles  form  at  either  or  both  plates?     Press  the  free  end 
of  the  wire  against  the  other  plate,  and  observe  whether  bubbles 
form  at  both  plates.     Remove  the  end  of  the  wire,  and  observe. 
Repeat  till  sure  of  results.     Avoid  inhaling  the  unpleasant  fumes 
from  the  battery. 

The  appearance  of  bubbles  on  the  copper  plate  is  not  in  itself 
evidence  of  chemical  action  on  that  plate.  If  there  is  such  chemi- 
cal action,  the  copper  plate  will  be  consumed  after  repeated  use,  as 
the  zinc  is,  and  the  liquid  will  become  greenish  blue.  Conclusion? 

d.  Connect  the  plates  by  means  of  the  wire,  using  the  clamps 
or  double  connector.     (Do  not  twist  wires  together.     Connections 


THE   SIMPLE    VOLTAIC   CELL 


193 


must  always  be  made  to  the  bare  wire ;  for  the  current  will  not 
pass  through  the  insulation  covering  the  wire.)  Extend  a  portion 
of  the  wire  parallel  to  the  magnetic  needle  and  several  inches 
above  it.  Lower  the  wire  without  changing  its  direction  (Fig.  91), 
and  note  the  behavior 
of  the  needle  as  the  wire 
approaches  it.  Note 
the  effect  of  holding  the 
wire  under  the  needle. 
Disconnect  the  wire 
from  one  of  the  plates, 
and  repeat.  Result? 

The  deflection  of  the 
needle  indicates  the  ex- 
istence of  a  magnetic 
field  about  the  wire,  due 
to  an  electric  current  flowing  through  the  wire  from  the  copper 
to  the  zinc.  (Since  copper  is  not  magnetic,  it  is  evident  that  the 
wire  is  not  magnetized.) 

e.  Connect  the  plates  again,  and  estimate  the  relative  amounts 
of  hydrogen  liberated  at  the  two  plates.  The  hydrogen  liberated 
at  the  copper  plate  represents  chemical  action  (of  the  acid  on  the 
zinc  plate)  which  maintains  the  electric  current  in  the  wire.  This 
is  useful  action,  i.e.  action  by  which  an  electric  battery  serves  its 
intended  purpose.  The  hydrogen  liberated  at  the  zinc  plate 
represents  local  action  (see  text),  which  plays  no  part  in  main- 
taining the  current  in  the  wire,  and  hence  results  in  wasted 
energy.  Estimate  the  relative  amounts  of  useful  and  wasteful 
action.  Remove  the  zinc  from  the  acid. 

Experiment  114.  —  To  determine  the  effect  of  amalgamating  the 
zinc. 

Experimental  Work.  —  a.    Place  the  amalgamated  zinc  and  the 
copper  plates  in  the  acid.     With  the  plates  disconnected  (circuit 
open),  observe  the  size  and  abundance  of  the  bubbles  forming  on 
COLEMAN'S  NEW  MANUAL — 13 


194  ELECTRICITY 

the  zinc  plate.     Compare  with  the  results  obtained  with  the  un- 
amalgamated  zinc  in  a  above. 

b.  Connect  the  plates  with  the  wire,  and  test  the  presence  of 
an  electric  current,  as  in  d  above. 

c.  Estimate  the  relative  amount  of  useful  and  wasteful  action, 
as  you  did  with  the  unamalgamated  zinc  in  e  above. 

Place  all  the  plates  on  the  tray  (or  in  the  empty  tumbler),  being 
careful  not  to  let  the  amalgamated  zinc  touch  the  other  plates. 


EXERCISE   60.    THE    MAGNETIC    FIELD    OF   A 
CURRENT 

References.  —  Adams,  472-473,  475  ;  Coleman,  453-455  ;  Car. 
&  C.,  433-434,  452-454;  Ches.  G.  &  T.,  373;  Hoad.  Br.,  371- 
373  ;  Hoad.  EL,  408-409  ;  Mumper,  257-258  ;  Jackson,  119-124  ; 
Mil.  &  G.,  355,  394-395  j  Went.  &  H.,  278,  281. 

Apparatus.  —  Small  compass;  wire  rectangle  (Fig.  92);  square 
of  cardboard  with  slit  from  edge  to  hole  at  center ;  electric  cell ; 
tangent  galvanometer  or  a  flat,  circular  coil,  with  cardboard  to  fit, 
as  in  Figure  93  ;  fine  iron  filings  in  sifter ;  contact  key  (useful, 
but  may  be  omitted). 

[The  wire  rectangle  should  consist  of  8  or  10  turns  of  No.  16, 
or  20  to  30  turns  of  No.  20  to  24  copper  wire.  The  galvanometer 
should  have  15  turns.  A  flat,  circular  coil  of  15  to  20  turns  and 
12  to  15  cm.  in  diameter  will  serve  instead.  A  good  dry  cell  (as 
the  Columbia),  a  Grenet,  or  a  Fuller  cell  will  furnish  sufficient 
current.  These  cells  all  have  a  very  low  resistance,  which  is 
necessary.] 

CAUTION.  Throughout  this  exercise  the  circuit  should  be  open 
when  the  current  is  not  required,  to  avoid  waste  and  to  reduce 
polarization.  If  a  Grenet  cell  is  used,  the  circuit  is  closed  by 
lowering  the  zinc  into  the  liquid,  and  opened  by  raising  it.  Keep 
the  zinc  raised  when  the  current  is  not  in  immediate  use.  If  a  dry 
cell  is  used  and  a  contact  key  provided,  always  include  the  con- 


THE   MAGNETIC   FIELD   OF  A  CURRENT 


195 


tact  key  in  the  circuit.  The  circuit  is  opened  and  closed  at  the  key. 
If  a  key  is  not  provided,  close  the  circuit  by  holding  an  end  of 
the  wire  against  a  post  of  the  cell.  If  the  wire  is  not  fastened, 
there  will  be  less  probability  of  keeping  the  circuit  closed  unnec- 
essarily. A  good  dry  cell  furnishes  a  large  current  through  cir- 
cuits of  low  resistance,  as  in  this  exercise,  if  the  service  required 
is  brief,  with  intervals  of  rest  to  permit  recovery  from  polarization. 

Experiment  115. —  To  find  the  shape  and  direction  of  the  lines 
of  force  about  a  straight  conductor  carrying  a  current,  and  the 
relation  between  their  direction  and  the  direction  of  the  current. 

Experimental  Work.  —  a.    Support  the  cardboard  in  a  horizon- 
tal position  with  one  side  of  the  wire  rectangle  passing  through 
the  hole  at  its  center,  and  sprinkle 
iron  filings  on  it.     Connect  the  rec- 
tangle with  the  electric  cell,  including 
the  contact  key  in  the  circuit,  if  one 
is  provided. 

The  current  leaves  the  cell  from  the 
carbon  terminal  and  returns  through 
the  zinc  terminal.     Determine  from 
this   fact  whether  the  current  flows       / 
up  or  down  on  the  side  of  the  rec-    / 
tangle  where  the  cardboard  is  placed. 
(The  current  flows  in  the  same  direc- 
tion round  the  rectangle  through  all  the  turns  composing  it.) 

With  the  circuit  closed,  tap  the  cardboard  gently  until  the 
filings  are  arranged  in  distinct  lines.  Use  the  compass  to  deter- 
mine the  direction  of  the  lines  of  force  round  the  wire  (i.e.  the 
direction  round  the  wire  in  which  the  north  pole  of  the  needle 
points).  Break  the  circuit.  Raise  the  zinc,  if  you  are  using  a 
Grenet  cell.  Return  the  filings  to  the  sifter. 

Draw  a  figure  in  perspective,  showing  with  arrowheads  the 
direction  of  the  current  and  the  direction  of  the  lines  of  force. 

Several  turns  of  wire  are  used  in  the  rectangle  merely  to  increase 


FIG.  92. 


196  ELECTRICITY 

the  effect  of  the  current.  The  magnetic  field  is  strengthened  in 
proportion  to  the  number  of  turns,  but  is  otherwise  the  same  as 
that  about  a  single  wire. 

b.  Grasp  the  wire  above  the  cardboard  with  the  right  hand, 
with  the  thumb  extended  (up  or  down)  in  the  direction  in  which 
the  current  was  flowing.  Do  the  fingers  point  round  the  wire  in 
the  direction  of  the  lines  of  force  (as  the  north  pole  of  the  com- 
pass needle  points)  or  in  the  opposite  direction  ?  The  relation 
between  the  direction  of  an  electric  current  in  a  straight  con- 
ductor and  the  direction  of  the  lines  of  force  round  the  conductor, 
when  stated  with  reference  to  the  thumb  and  fingers  of  the  right 
hand,  is  known  as  the  right-hand  rule.  State  it  in  full. 

c.  Close  the  circuit,  and  use 
the  compass  to  determine  the 
direction  of  the  lines  of  force 
round  the  opposite  side  of  the 
rectangle.     Is  their  direction  in 
agreement  with  the  right-hand 
rule? 

d.  Observe  the  direction  of 
the   north  pole  of  the   needle 
with  reference  to  the  wire,  when 
held  just  above  the  upper  side 

of  the  rectangle  and  when  held  just  below  it.  Repeat  with  the  rec- 
tangle standing  in  various  directions,  including  east-west  and  north- 
south.  Is  the  behavior  of  the  needle  in  agreement  with  the  rule  ? 

Experiment  116.  —  To  study  the  magnetic  field  within  and 
about  a  coil  of  wire  carrying  a  current,  with  special  reference  to 
the  relation  between  the  direction  of  the  current  round  the  coil  and 
the  direction  of  the  lines  of  force  at  its  center. 

Experimental  Work.  —  a.  Connect  the  cell  to  the  two  binding 
posts  of  the  galvanometer  between  which  all  the  turns  of  the  coil 
are  included.  Adjust  the  cardboard  to  the  middle  of  the  coil 
(Fig.  93),  and  close  the  circuit.  Sprinkle  filings  on  the  card- 


THE    HELIX,   ELECTRO-MAGNET,   AND   ELECTRIC  BELL     197 

board,  and  tap  with  the  finger.  Determine  with  the  compass 
the  direction  of  the  lines  of  force  through  the  coil.  Break 
the  circuit. 

If  the  direction  in  which  the  wire  is  wound  round  the  coil  from 
one  post  to  the  other  is  open  to  view,  find  from  the  connections 
with  the  cell  in  which  direction  the  current  was  flowing  round  the 
coil.  If  the  winding  of  the  coil  is  not  open  to  view,  find  the 
direction  of  the  current  round  the  coil  from  the  right-hand  rule 
and  the  known  direction  of  the  lines  of  force.  (The  rule  applies 
to  the  parts  of  a  curved  conductor  as  well  as  to  a  straight  one,  as 
the  change  in  the  field  caused  by  the  .bending  of  the  conductor 
does  not  alter  the  relation  expressed  by  the  rule.)  Draw  a  figure 
in  perspective,  showing  the  direction  of  the  current  and  the  di- 
rection of  the  lines  of  force  within  and  about  the  coil.  Return 
the  filings  to  the  sifter. 

b.  As  applied  to  coils,  a  different  statement  of  the  right-hand 
rule  is  more  convenient.  Close  the  right  hand  and  place  it  within 
the  coil,  with  the  extended  thumb  pointing  in  the  direction  of  the 
lines  of  force  through  the  coil.  Do  the  fingers  point  in  the  direc- 
tion of  the  current  round  the  coil  or  in  the  opposite  direction? 
State  the  rule  in  full. 

EXERCISE  61.    THE  HELIX,  THE  ELECTRO-MAGNET, 
AND   THE   ELECTRIC   BELL 

References.  —  Adams,  478-483  ;  Coleman,  456-458  ;  Car.  &  C., 
455,457-458,515;  Ches.  G.  &  T.,  393,  442  ;  Hoad.  Br.,  373-376, 
418;  Hoad.  EL,  410-414,  460;  Mumper,  262,  266;  Jackson,  124- 
129,  319;  Mil.  &  G.,  396-400;  Went.  &  H.,  282,  284-285. 

Experiment  117.     To  study  the  helix  and  the  electro-magnet: 

Apparatus.  —  Soft  iron  rod  of  smaller  diameter  than  a  lead  pen- 
cil; 3  m.  of  small  (No.  20  to  24)  double-covered,  copper  wire; 
coarse  iron  turnings,  tacks  or  small  nails ;  magnetic  needle ;  dry, 
Grenet,  or  Fuller  cell. 


198  ELECTRICITY 

Experimental  Work.  —  a.  Wrap  half  the  wire  round  a  lead 
pencil,  forming  a  close  coil  of  one  or  more  layers  and  about  5  cm. 
long.  Connect  the  wire  with  the  cell,  and  find  by  means  of  the 
magnetic  needle  which  end  of  the  coil  acts  like  the  north  pole 
of  a  magnet  and  which  like  the  south  pole.  Break  the  circuit. 
Trace  the  direction  of  the  current  from  the  cell,  and  find  which 
way  it  flowed  round  the  coil.  Grasp  the  coil  in  the  right  hand, 
with  the  fingers  pointing  round  it  in  the  direction  of  the  current, 
and  the  thumb  extended.  Does  the  thumb  point  in  the  direction 
of  the  north  pole  or  the  south  pole  of  the  coil?  State  the  rela- 
tion in  full. 

Show  that  this  relation  amounts  to  the  same  thing  as  the  one 
obtained  with  the  flat  coil  in  the  preceding  experiment. 

b.  Remove  the  helix  from  the  pencil,  and  slip  it  over  the  iron 
rod,  leaving  about  2  cm.  of  an  end  of  the  rod  exposed.     With 
the  circuit  open,  test  the  rod  for  magnetization  by  dipping  an 
end  of  it  into  the   iron   turnings   (or  tacks).     Close  the   circuit 
through  the  helix  and  repeat  the  test,  noting  carefully  the  quan- 
tity of  turnings  that  cling  to  the  rod.     Observe  the  behavior  of 
these  turnings  as  you  break  the  circuit.     What  does  this  behavior 
indicate?  -The  helix  and  the  rod  together  constitute  an  electro- 
magnet. 

c.  Wrap  the   remainder  of  the  wire  round  the   rod,  leaving 
only  a  few  inches  at  the  ends  for  convenient  connection  with 
the  cell.     (If  more  convenient,  replace  the  helix  on  the  pencil 
to  complete  the  winding.)     Note   the   quantity  of  turnings  that 
the  electro-magnet  will  now  pick  up  when  the  circuit  is  closed. 
How  has  the  strength   of  the  electro-magnet  been    affected    by 
increasing  the  number  of  turns  in  the  helix?     Account  for  this 
effect. 

d.  With  the  circuit  closed,  test  the  polarity  of  the  electro- mag- 
net by  means  of  the  magnetic  needle.     Do  like  poles  of  the  elec- 
tro-magnet and  the  helix  point  in  the  same  or  in  opposite  directions? 
(If  necessary,  repeat  the  test  of  the  helix  alone.)     Leave  the  cell 

.  disconnected. 


THE   HELIX,  ELECTRO-MAGNET,  AND    ELECTRIC   BELL      199 

Experiment  118.  —  To  study  the  construction  and  action  of  an 
electric  bell. 

Apparatus.  —  An  electric  bell  with  a  short  piece  of  rubber  tub- 
ing on  the  clapper  to  deaden  the  sound ;  push  button ;  connect- 
ing wires  ;  dry,  Leclanche*,  or  Fuller  cell. 

Experimental  Work. — a.  Connect  the  cell  with  the  bell, 
including  the  push  button  in  the  circuit.  If  the  push  button  is 
not  provided,  close  the  circuit  by  touching  an  end  of  the  wire  to 
one  of  the  poles  of  the  cell.  Ring  the  bell,  and  observe  the  sparks 
at  the  point  where  the  spring  that  is  attached  to  the  clapper  touches 
the  point  of  a  screw.  The  current  crosses  at  this  point ;  hence 
the  circuit  is  broken  whenever  the  spring  leaves  the  screw. 

Trace  the  circuit  through  the  bell  from  either  binding  post  to 
the  other.  The  metal  frame  of  the  bell  commonly  forms  a  part 
of  the  circuit.  Does  it  in  this  bell?  There  are  four  posts  whose 
attachment  to  the  base  must  be  carefully  examined.  They  are 
the  two  binding  posts,  the  post  that  carries  the  screw  that  touches 
the  spring,  and  the  upright  to  which  the  clapper  is  attached. 
One  or  more  of  these  will  be  found  to  be  electrically  insulated 
from  the  base  by  means  of  hard  rubber  washers.  Such  a  post  is 
not  in  metallic  contact  with  the  base,  and  the  current  cannot  pass 
between  them.  The  current  is  thus  compelled  to  follow  a  definite 
course  through  the.  bell.  Describe  this  course,  referring  to  a  sim- 
plified lettered  diagram.  Mark  the  insulated  posts  in  this  diagram, 
and  represent  by  a  dotted  line  the  part  of  the  circuit  formed  by 
the  metal  base  of  the  bell. 

What  wires  would  you  supply  to  complete  the  circuit  if  the  base 
were  of  wood,  and  hence  could  not 'be  utilized  as  a  part  of  the 
circuit? 

b.  Explain  the  action  of  the  bell.     How  would  the  bell  behave 
if  the  circuit  were  such  as  to  send  the  current  through  the  electro- 
magnet without  crossing  between  the  screw  and  the  spring? 

c.  Unscrew  the  cap  of  the  push  button,  and  observe  its  con- 
struction.    Describe. 


200  ELECTRICITY 

EXERCISE    62.     THE   ELECTRIC   TELEGRAPH 

References —  Adams,  484-486  ;  Coleman,  459-463  ;  Car.  &  C., 
507-514  ;  Ches.  G.  &  T.,  444-445  ;  Hoad.  Br.,  419-427  ;  Hoad. 
EL,  461-468;  Mumper,  264-265  ;  Jackson,  290-299;  Mil.  &  G., 
401-403  ;  Went.  &  H.,  286. 

Experiment  1 19.  -•—  To  set  up  a  short  distance  telegraph  line,  and 
to  study  the  construction  and  action  of  the  instruments. 

Apparatus.  —  Two  sounders  ;  two  keys  ;  two  gravity  cells  ;  con- 
necting wires. 

Experimental  Work.  —  a.  Examine  the  sounder.  Send  the  cur- 
rent from  a  gravity  cell  through  it  alone.*  The  lever  should  be 
drawn  down.  Why?  If  it  is  not,  the  spring  probably  needs 
adjusting.  Does  the  movement  of  the  lever  break  the  circuit,  as 
it  does  in  the  electric  bell? 

b.  Examine  the  key.     Find  the  insulation  that  keeps  the  circuit 
open  in  the  key  when  the  switch  is  open  and  the  lever  up.     Trace 
the  circuit  through  the  key  (i)  when  the  switch  is  open  and  the 
lever  depressed  ;  (2)  when  the  lever  is  up  and  the  switch  closed. 
Place  the  key  in  circuit  with  the  sounder,  and  operate  the  sounder 
by  means  of  it. 

c.  Connect  up  a  telegraph  line  of  two  stations,  having  a  sounder, 
a  key,  and  a  gravity   cell  at  each  station.     The  cells  must  be 
connected  so  as  to  act  in  the  same  direction  round  the  circuit. 
Operate  the  line  from  each  station  in  turn.     Why  is  one  key  kept 
closed  by  means  of  the  switch  while  the  other  key  is  in  use  ? 

Make  a  diagram  of  the  circuit. 

If  gravity  cells  are  used,  leave  them  on  closed  circuit  through 
the  sounders  when  you  have  finished. 

Experiment  1 20.  —  To  set  up  a  long  distance  telegraph  line  ;  and 
to  study  the  construction  and  action  of  the  relay. 

Apparatus.  —  Two  sounders  ;  two  keys  ;  two  relays  ;  four  to  six 
gravity  cells,  as  needed  ;  connecting  wires. 


THE   ELECTRIC   TELEGRAPH 


201 


Experimental  Work.  —  a.  Examine  the  relay.  Find  the  posts 
by  which  the  line  circuit  is  connected  with  the  electro-magnet. 
The  local  circuit,  consisting  of  the  sounder  and  the  local  battery, 
is  connected  with  the  other  two  posts.  Trace  the  local  circuit 
between  these  posts,  and  find  where  and  how  it  is  closed  and 
opened  by  the  movement  of  the  vertical  lever. 

b.  Connect  the  local  circuit  with  the  relay,  using  only  one  cell, 
if  this  is  sufficient  to  operate  the  sounder.  Operate  the  sounder 
by  moving  the  lever  of  the  relay  back  and  forth  by  hand.  How 
is  this  possible  ? 


SOUNDER 


SOUNDER 


KEY 


-H 

LOCAL  BATTERY 


EARTH 


LOCAL  BATTERY 


EARTH 


FIG.  94. 


c.  Connect  up  the  local  circuits  at  the  two  stations  and  the  line 
circuit  between  them,  as  shown  in  Figure  94,  using  wire  for  the 
entire  line  circuit  instead  of  the  earth  for  the  return.  Open  the 
switch  at  one  station  and  operate  it,  at  the  same  time  observing 
the  action  of  the  relay  and  the  sounder,  another  pupil  also  ob- 
serving the  action  of  the  instruments  at  the  other  station.  Now 
let  the  other  pupil  operate  the  key  at  his  station,  both  observing 
as  before. 

Make  a  diagram  of  the  entire  telegraph  system  as  you  have 
arranged  it. 

If  gravity  cells  are  used,  leave  the  switches  closed  when  you 
have  finished ;  if  other  cells  are  used,  disconnect  them  or  leave 
the  switches  open. 


202 


ELECTRICITY 


EXERCISE  63.  THE  TANGENT  GALVANOMETER; 
POLARIZING  AND  NONPOLARIZING  OR  CONSTANT 
CELLS 

References Adams,  465-470,  489  ;  Coleman,  448-452,  464- 

467;  Car.  &  C.,  436-442,  464-466,  471-472;  Ches.  G.  &  T., 
384-386,  400-402;  Hoad.  Br.,  351-355,  382;  Hoad.  EL,  392- 
398;  Mumper,  254-256,  260,  282  ;  Jackson,  40-50,  145  ;  Mil.  & 
G.,  378-383;  Went.  &  EL,  275-276,  280. 

Principle  of  the  Tangent  Galvanometer.  —  In  the  tangent  gal- 
vanometer (Fig.  95)  the  current  is  sent  through  a  vertical  circular 
*  coil,  consisting  of  one  or  more 

turns  of  insulated  wire.  A  com- 
pass, with  a  scale  graduated  in 
degrees,  is  placed  at  the  center 
of  the  coil.  In  Experiment  116 
it  was  found  that  the  lines  of 
force  due  to  a  current  in  a  cir- 
cular coil  are  approximately 
straight  near  the  center  of  the 
coil,  and  are  at  right  angles  to 
the  plane  of  the  coil.  The 
magnetic  field  of  the  current  is 
of  sensibly  uniform  strength 
throughout  this  small  space  at 
the  center ;  and,  in  a  good 
FIG.  95.  instrument,  the  compass  needle 

is  short  (not  above  2  cm.)  in 

order  that  it  may  lie  wholly  in  this  uniform  field,  in  whatever 
direction  it  may  turn.  The  deflection  of  the  needle  is  found  by 
means  of  a  long  pointer,  which  is  attached  at  right  angles  to  the 
needle,  and  turns  with  it.  All  parts  of  the  instrument  except  the 
needle  must  be  nonmagnetic.  The  pointer  is  generally  of  alu- 
minum, on  account  of  its  lightness. 


THE  TANGENT  GALVANOMETER 


203 


In  using  a  tangent  galvanometer  it  must  be  placed  with  the 

plane  of  its  coil  in  the  magnetic  meridian ;  in  which  position  the 

lines  of  force  of  the  coil  at  its  center  (where 

the  needle  is)  are  at  right  angles  to  the  lines 

of  force    of  the    earth's  field.     When  the 

galvanometer  is  in  this  adjustment  and  no 

current  is  flowing,  the  earth's  field   brings 

the  needle  to  rest  in  the  plane  of  the  coil 

(along  the  line  NS  in  Figure  96).     When 

the  current    is  flowing,    its    magnetic   field 

tends  to  set  the  needle  a't  right  angles  to 

this    position.     Thus   two  forces,  acting  at 

right  angles  to  each  other,  are  exerted  on 

each  pole   of  the  needle,   as  shown  in  the 

figure  ;  and  the  needle  comes  to  rest  in  the  R 

direction  of  the  resultant  of  these  forces. 

The  deflection  of  the  needle  caused  by  the 

current  is  the  angle  NOR.  FlG-  96- 

In  Figure  97  ON  represents  the  earth's  magnetic  force  (acting 

on  the  north  pole  of  the  compass  needle),  and  OB  the  magnetic 

force  due  to  a  current 

N  A  X  A"     in  the   coil.     The  de- 

flection in  this  case  is 
NO  A  or  a.  Now,  if 
the  current  is  doubled, 
its  magnetic  force  is 
doubled,  as  represented 
by  O£' ;  and  the  de- 
flection becomes  NO  A 
or  a'.  Similarly,  if  the 


B 


FIG.  97. 


B 


B 


current  is  increased  to  three  times  its  first  strength,  its  magnetic 
force  is  also  trebled,  as  represented  by  OB11,  and  the  deflection 
becomes  NOB"  or  a".  It  is  evident  from  the  figure  that  the 
deflection  increases  less  rapidly  than  the  current  (a'  <2  a  and 
a"  <  3  #)  •  the  current  is  not  proportional  to  the  deflection.  But 


204  ELECTRICITY 

the-  tangent1  of  angle  af  is  twice  the  tangent  of  angle  a  (i.e. 
NA'/ON=  2  NA/ON),  and  the  tangent  of  a"  is  three  times  the 
tangent  of  a  (i.e.  NA"/ON  =  3  NA/ON}.  This  relation  is 
expressed  in  general  terms  as  follows  :  When  currents  of  different 
strengths  are  sent  through  the  same  number  of  turns  of  the  coil  of  a 
tangent  galvanometer,  the  currents  are  proportional  to  the  tangents 
of  the  angles  of  deflection  which  they  produce.  This  is  why  the 
instrument  is  called  a  tangent  galvanometer. 

To  express  this  relation  algebraically,  let  C  and  O  denote  the 
strengths  of  two  currents  (measured  in  amperes),  and  let  a  and  a' 
denote  the  deflections  which  they  produce  when  sent  through  the 
same  number  of  turns  of  a  tangent  galvanometer ;  then 

C  \  O  :  :  tan  a  :  tan  a', 

in  which  "tan  a "  is  the  usual  abbreviation  for  "tangent  of 
angle  a.11 

EXAMPLE.  A  current  C  causes  a  deflection  of  50°,  and  another 
current  C  causes  a  deflection  of  25°.  It  is  found  from  a  table  of 
tangents  that  tan  50°  =  1.19  and  tan  25°  =  .466. 

Hence  C:  C  :  :  1.19  :  .466  ; 

from  which  C=  2.55  C. 

1  The  ratio  of  one  leg  of  a  right  triangle  to  the  other  is  called  the  tangent  of 
the  angle  opposite  to  the  first  leg.  Thus  the  tangent  of  angle  A  (Fig.  98)  is 

BCiACor:  B'C':  AC',  BC  and  B'C 
being  any  line  perpendicular  to  either 
side  of  the  given  angle.  Since  triangles 
AB C  and  AB1 C1  are  similar,  the  ratios 
BC/AC&nd  B'C'/AC'  are  equal.  It 
is  evident,  therefore,  that  the  tangent 
of  an  angle  is  a  definite  quantity,  the 
value  of  which  depends  only  upon  the 
size  of  the  angle.  Angles  are  not  pro- 

FIG.  98.  portional   to  their  tangents,    although 

small  angles  are  very  nearly  so.     The 

tangent  of  any  angle  from  o°  to  90°  may  be  found  from  a  table  of  tangents 
(Appendix,  Table  XV). 


THE   TANGENT   GALVANOMETER 


205 


A  tangent  galvanometer  having  a  scale  graduated  in  degrees 
may  be  thus  used  to  determine  the  relative  strengths  of  currents, 
but  it  does  not  give  their  numerical  values.  The  numerical  value 
(in  amperes)  may,  however,  be  obtained  by  multiplying  the  tangent 
of  the  angle  of  deflection  by  a  constant  factor,  found  by  experiment. 

To  adjust  the  Galvanometer.  — -  The  galvanometer  is  turned  so 
that  the  two  ends  of  the  pointer  stand  at  the  two  zero  points  of 
the  circular  scale.  Since  the  two  zero  points  are  in  a  line  per- 
pendicular to  the  plane  of  the  coil  and  the  pointer  is  at  right 
angles  to  the  magnetic  needle,  this  adjustment  brings  the  plane 
of  the  coil  into  the  magnetic  meridian. .  This  adjustment  must  not 
be  disturbed  during  an  experiment.  All  magnetic  substances  must 
be  kept  at  a  distance  in  adjusting  and  using  the  galvanometer. 

To  find  the  Deflection. — With  most  instruments  it  will  be 
found  that  the  two  ends  of  the  pointer  do  not  stand  exactly  at 
the  zero  points  at  the  same  time,  that  the  two  ends  of  the  pointer 
give  slightly  different  readings  for  the  same  deflection,  and  that 
when  the  current  is  reversed  in  the  coil,  causing  a  deflection  in 
the  opposite  direction,  the  two  readings  of  this  deflection  differ 
not  only  from  each  other,  but  also  from  the  first  two  readings. 
These  discrepancies  frequently  amount  to  one  or  two  degrees,  and 
are  due  to  various  slight  imperfections  in  the  construction  of  the 
compass,  and  to  an  inexact  adjustment  of  the  instrument.  To 
find  the  true  value  of  the  deflection  due  to  a  given  current  it  is 
therefore  necessary  to  read  the  position  of  both  ends  of  the 
pointer,  then  to  reverse  the  current  and  take  two  readings  as 
before,  and  finally  to  take  the  average  of  these  four  readings  as 
the  true  deflection. 

Before  taking  a  reading,  the  cover  of  the  compass  should  be 
gently  tapped  with  the  finger  to  overcome  friction,  which  might 
otherwise  hold  the  needle  in  a  wrong  position 

A  reading  should  be  taken  with  one  eye  closed  and  the  other 
held  vertically  above  the  pointer,  otherwise  the  pointer  will  not 
appear  in  its  true  position  over  the  scale.'  The  eye  is  in  the  cor- 


206  ELECTRICITY 

rect  position  when  the  faint  image  of  it,  formed  by  reflection 
from  the  glass  cover  of  the  compass,  is  directly  under  the  pointer. 
If  the  scale  is  graduated  in  single  degrees,  the  reading  should  be 
estimated  to  tenths  of  a  degree ;  if  graduated  in  intervals  of  two  de- 
grees each,  the  reading  should  be  taken  to  the  nearest  half  degree. 

Use  of  Different  Numbers  of  Turns  of  the  Coil.  —  The  coil  of  a 
tangent  galvanometer  usually  consists  of  fifteen  turns,  which  are 
connected  in  groups  of  five  to  binding  posts,  so  that  the  current 
can  be  sent  through  five,,  ten,  or  all  fifteen  turns,  as  desired. 
The  number  of  turns  used  in  any  experiment  should  be  the  one 
giving  deflections  nearest  to  45°,  for  the  work  is  less  accurate 
with  either  very  large  or  very  small  deflections.  A  given  error 
in  reading  the  deflection  involves  the  least  error  in  the  computed 
current  when  the  deflections  are  between  30°  and  60°. 

It  is  important  to  understand  why  the  deflection  varies  with  the 
number  of  turns  used.  The  tangent  of  the  angle  of  deflection  is 
proportional  to  the  magnetic  force  of  the  current ;  and,  with  a 
current  of  given  strength,  this  magnetic  force  is  proportional  to 
the  number  of  turns  through  which  the  current  flows. 

Experiment  121. —  To  determine  the  decrease  of  current  strength 
due  to  polarization  in  different  cells  under  the  same  conditions. 

Apparatus.  —  Tangent  galvanometer;  constant  cell  (gravity  or 
Daniell)  ;  simple  cell,  as  in  Exercise  59;  one  or  more  cells  for 
open  circuit  work  (dry,  Leclanche*,  Grenet,  etc.) ;  coil  of  wire 
having  a  resistance  of  about  3  ohms,  with  double  connectors ; 
connecting  wires;  watch  or  clock  with  second-hand. 

[A  tangent  galvanometer  to  be  satisfactory  for  students'  use 
must  conform  to  the  following  requirements :  coil  not  less  than 
6  in.  in  diameter,  having  10  or  15  turns  in  at  least  three  combina- 
tions (usually  5,  10,  and  15);  short  magnetic  needle,  with  agate 
cap  and  light  aluminum  pointer ;  dial  not  less  than  3  hi.  in  diam- 
eter, and  graduated  in  single  degrees.  Such  an  instrument  will 
cost  from  $6.00  to  $10.00.] 

CAUTION.     With  considerable  resistance  in  the  circuit,  the  cur- 


THE  TANGENT  GALVANOMETER          2O/ 

rent  from  a  cell  is  small,  and  there  is  but  little  chemical  action  in 
the  cell.  Under  such  conditions  polarization  takes  place  slowly. 
When  a  cell  is  short-circuited  (i.e.  placed  in  a  circuit  having 
almost  no  resistance),  the  current  is  as  large  as  the  cell  is  capable 
of,  and  polarization  takes  place  rapidly,  if  at  all.  When  a  simple 
cell  is  short-circuited,  polarization  is  practically  instantaneous. 
Hence  in  connecting  up  the  different  cells  in  the  following  ex- 
periment, care  must  be  taken  to  include  the  resistance  coil  in  the 
circuit  before  the  circuit  is  closed.  The  experiment  with  the 
simple  cell  will  fail  completely  if  this  precaution  is  not  observed. 
The  copper  plate  can  be  depolarized  by  heating  it  in  a  Bunsen 
flame.  Wiping  it  with  a  cloth  is  not  effective. 

Experimental  Work.  —  Adjust  the  galvanometer.  Connect  the 
simple  cell  with  ten  turns  of  the  galvanometer  coil,  including  the 
resistance  coil  (3  ohms)  in  the  circuit.  Read  the  deflection  in- 
dicated by  one  end  of  the  pointer  as  quickly  as  possible;  and 
after  one  minute  (by  a  clock  or  watch),  read  the  deflection  again, 
meanwhile  observing  the  behavior  of  the  needle.  Remember 
always  to  tap  the  cover  of  the  compass  lightly  with  the  finger  be- 
fore taking  a  reading.  (In  this  exercise  it  is  sufficiently  accurate 
to  take  only  one  reading  of  a  deflection,  always  reading  the  same 
end  of  the  pointer,  with  the  deflection  in  the  same  direction.) 

Immediately  after  taking  the  second  reading,  bring  the  binding 
screws  (double  connectors)  at  the  ends  of  the  resistance  coil  to- 
gether, and  hold  them  in  firm  contact  for  one  minute.  This 
throws  the  resistance  coil  out  of  the  circuit,  and  short-circuits 
the  cell.  Polarization,  if  not  already  completed  before  the  short- 
circuiting,  will  now  take  place  very  rapidly  (for  reasons  stated  in 
the  caution  above).  After  one  minute  separate  the  binding  screws, 
thus  restoring  the  circuit  as  at  first,  and  read  the  deflection. 
Record  as  indicated  below.  Remove  the  plates  from  the  cell. 

Repeat  the  above  experiment  with  each  of  the  cells  provided, 
using  in  each  case  the  number  of  turns  of  the  galvanometer  coil 
that  will  give  a  deflection  between  30°  and  60°,  or  as  nearly 


208 


ELECTRICITY 


within  these  limits  as  possible.  With  a  dry  or  a  Grenet  cell,  try 
5  turns  first;  with  a  Leclanche"  cell,  10  turns;  with  a  gravity  or 
a  Daniell  cell,  15  turns. 

Data  and  Computations.  —  Record  observations  and  computa- 
tions as  follows  :  — 


SIMPLE 

GRAVITY 

DRY 

ETC. 

No.  of  turns  of  galvanometer  coil  used 

Deflection  on  closing  circuit  through  resist- 
ance coil  of  3  ohms        .... 

Deflection,  same  circuit,  after  it  has  been 









Deflection,  same  circuit,  after  cell  has  been 
on  short  circuit  I  min. 









COMPUTATIONS 

Tangent  of  first  deflection 
Tangent  of  second  deflection    .         .         . 
Tangent  of  third  deflection 

Percentage  of  decrease  of  current  in  I  min. 
through  resistance  coil 

Percentage  of  decrease  of  current  in  I  min. 









Discussion.  —  i.    Name  the  cells  used  in  the  order  of  rapidity 
v/ith  which  they  polarize. 

2.  Account    for   the   positions   that   the   simple   cell   and  the 
gravity  (or  Daniell)  cell  occupy  in  this  list. 

3.  With  which  cells  is  the  decrease  of  current  greater  on  short 
circuit  than  with  the  resistance  coil  in  the  circuit?     Why?     With 
which  cells  (if  any)  is  it  less,  and  why? 

4.  What  means  are  employed  in  the  different  cells  to  reduce 
or  prevent  polarization  ?     (See  text.) 


MEASUREMENT  OF   RESISTANCE   BY   SUBSTITUTION       2OQ 


EXERCISE   64.       MEASUREMENT   OF   RESISTANCE    BY 
SUBSTITUTION;  THE  LAWS  OF  RESISTANCE1 

References Adams,   492-495;    Coleman,   468-471;    Car.  & 

C.,  460-462,  464-466;  Ches.  G.  &  T.,  406-407,  409-410; 
Hoad.  Br.,  377-380,  388;  Hoad.  El.  421-424;  Mumper,  275- 
277  ;  Jackson,  91-101,  160-161  ;  Mil.  &  G.,  363-365  ;  Went.  & 
H.,  290,  294. 

Method.  —  The  resistance  to  be  measured  is  connected  in  circuit 
with  the  galvanometer  and  a  constant  cell,  and  the  deflection 
read  as  accurately  as  possible.  The  unknown  resistance  is  then 
removed  from  the  circuit,  and  a  resistance  box  (Fig.  99)  put 
in  its  place.  Different  resist- 
ances are  introduced  into  the 
circuit  through  the  box,  by 
removing  plugs,  till  the  de- 
flection of  the  galvanometer 
is  the  same  as  before.  The 
sum  of  the  resistances  of  the 
box  then  included  in  the  cir- 
cuit is  equal  to  the  unknown 
resistance.  For  the  equal 
deflections  of  the  galvanom- 
eter indicate  that  the  same 
amount  of  current  flows  through  the  circuit  in  the  two  cases, 
and  the  cell  has  a  constant  E.  M.  F. ;  hence,  according  to  Ohm's 
Law,  the  total  resistance  of  the  circuit  must  be  the  same  in  the 
two  cases  (R  =  E/C)-y  hence,  further,  the  resistance  introduced 
from  the  box  must  be  equal  to  the  unknown  resistance,  no  change 
having  been  made  in  the  remainder  of  the  circuit.  The  two 
deflections  being  equal  and  in  the  same  direction,  a  single  reading 
(of  the  same  end  of  the  pointer)  for  each  deflection  is  sufficient. 


FIG.  99. 


1  Either  experiment  of  this  exercise  may  be  taken,  and  the  other  omitted. 
COLEMAN'S  NEW  MANUAL  — 14 


210  ELECTRICITY 

Resistances  obtained  by  this  method  may  be  in  error  by  as 
much  as  10%,  even  with  careful  work.  This  inaccuracy  is  due 
to  the  fact  that,  with  a  resistance  of  several  ohms  already  in 
the  circuit,  a  change  of  a  few  tenths  of  an  ohm  causes  hardly  a 
perceptible  change  in  the  deflection.  For  example,  the  deflec- 
tion may  be  right,  as  nearly  as  it  can  be  read,  with  a  resistance 
of  3  ohms  introduced  in  the  box,  while  an  additional  resistance 
of  .2  ohm  causes  no  perceptible  change.  Consequently,  the 
true  value  of  the  resistance  may  be  3  ohms,  3.2  ohms,  or  anything 
between,  making  a  possible  error  of  about  7%. 

Use  of  the  Resistance  Box —  The  resistance  of  the  row  of  brass 
plugs  and  blocks  on  the  resistance  box  is  practically  zero ;  but 
wherever  a  plug  is  removed,  the  resistance  of  the  coil  that  bridges 

the  gap  (Fig.  100)  is  introduced  in 
the  circuit.  The  amount  of  this  re- 
sistance is  marked  on  the  top  of 
the  box.  When  two  or  more  plugs 
are  removed,  the  resistance  intro- 
duced is  the  sum  of  the  resistances 
of  the  coils  where  the  plugs  are  out. 
In  finding  the  required  resistance, 

the  coils  are  tried  in  order  from  larger  to  smaller,  as  weights  are 
tried  in  weighing. 

Before  using  a  resistance  box,  turn  each  plug  in  its  hole,  while 
exerting  a  moderate  pressure.  This  insures  good  electrical  con- 
nection between  the  plugs  and  the  blocks,  which  is  necessary,  as 
the  resistance  at  the  points  of  contact  between  a  loose  plug  and  the 
adjacent  blocks  will  make  a  set  of  measurements  wholly  unreliable. 
A  switch  resistance  box  consists  of  three  series  of  resistances, 
with  a  switch  for  each  series.  A  resistance  is  introduced  by  turn- 
ing a  switch  so  as  to  rest  upon  the  contact  block  beside  which  the 
desired  number  of  ohms  is  marked.  The  total  resistance  intro- 
duced is  the  sum  of  the  numbers  at  the  three  contact  blocks  with 
which  the  switches  connect. 


MEASUREMENT   OF   RESISTANCE   BY   SUBSTITUTION       211 

Experiment  122.  —  To  measure  the  resistance  of  a  wire  by  the 
method  of  substitution. 

Apparatus — A  low  resistance  galvanometer;  constant  cell; 
resistance  box ;  two  coils  of  unknown  resistance ;  connecting 
wires. 

[Any  low-resistance  galvanometer  that  gives  a  suitable  deflec- 
tion may  be  used  instead  of  a  tangent  instrument.  An  error 
of  less  than  15%  or  20%  is  not  to  be  expected,  however,  unless 
the  dial  is  graduated  in  single  degrees.  With  a  gravity  or  a 
Daniell  cell  and  a  tangent  galvanometer  having  a  coil  of  15  turns, 
the  best  results  are  obtained  with  resistance  of  2  to  6  ohms.] 

Experimental  Work Adjust  the  galvanometer.  Complete 

the  circuit  through  the  cell,  the  galvanometer,  and  one  of  the 
unknown  resistances.  Use  the  number  of  turns  of  the  galva- 
nometer coil  which  gives  a  deflection  nearest  to  45°.  Read  the 
deflection  indicated  by  one  end  of  the  pointer,  estimating  tenths 
of  a  degree  as  accurately  as  possible.  Substitute  the  resistance 
box  for  the  unknown  resistance,  and  adjust  the  resistance  in 
it  till  the  deflection  (of  the  same  end  of  the  pointer  in  the 
same  direction)  is  exactly  the  same  as  before.  If  the  required 
resistance  is  uncertain  by  one  or  more  tenths  of  an  ohm,  find 
and  record  the  least  and  the  greatest  resistance  in  the  box  that 
give  the  correct  deflection,  and  take  their  average  as  the  value 
of  the  unknown  resistance.  If  the  deflection  is  seen  to  vary  when 
no  change  has  been  made  in  the  resistance  of  the  circuit,  the  cell 
is  at  fault  and  dependable  results  are  impossible.  Record  as  indi- 
cated below. 

Measure  in  the  same  way  the  other  unknown  resistance. 

Find  in  the  same  way  the  resistance  of  the  two  wires  when 
placed  together  in  the  circuit  so  that  the  whole  current  passes 
through  one  after  the  other.  (This  is  called  connecting  in  series.) 
The  resistance  of  the  two  wires  in  series  is  the  sum  of  their 
separate  resistances.  This  will  serve  as  a  test  of  the  accuracy  of 
your  results. 


2 1 2  ELECTRICITY 

Data  and  Computations.  — 


FIRST 
WIRE 

SECOND 
WIRE 

BOTH  IN 
SERIES 

Deflection      
Least  resistance  in  box  giving  an  equal  deflection 

Greatest    resistance    in   box    giving  an  equal 
deflection  ....;.. 

Average  resistance  in  box  giving  an  equal  de- 
flection (  =  resistance  of  wire)    . 







Sum  of  the  separate  resistances  of  wires 
Percentage  of  difference  between  sum  of  the  separate 
resistances  and  resistance  of  both  in  series 


=        ohms. 


Experiment  123. —  To  study  the  relation  between  the  resistance 
of  a  wire  and  its  length  and  diameter,  and  to  determine  the  relative 
resistance  of  German  silver  or  other  wire  and  copper  wire  of  the 
same  length  and  diameter. 

Apparatus.  —  Low-resistance  galvanometer;  constant  cell;  re- 
sistance box ;  three  pieces  of  wire  of  high  specific  resistance,  of 
equal  length,  and  two  of  them  of  the  same  diameter ;  copper  wire 
of  same  diameter  as  one  of  the  others,  and  long  enough  to  have  a 
nearly  equal  resistance. 

[Two  pieces,  i  m.  each,  of  No.  26  and  i  m.  of  No.  30,  all  of 
German  silver,  and  15  m.  of  insulated  copper  wire  of  either  num- 
ber are  suitable.  They  may  be  in  coils  or  stretched  on  a  board. 
If  stretched,  the  German  silver  wires  may  be  bare  or  covered. 
See  suggestions  under  Experiment  129  for  making  a  piece  of 
apparatus  (Fig.  101)  especially  suited  to  both  of  these  experi- 
ments.] 

Experimental  Work.  —  Following  the  directions  of  the  preced- 
ing experiment,  find  the  resistance  (a)  of  one  of  the  two  larger 
high-resistance  wires ;  (£)  of  the  two  larger  high- resistance  wires 


THE   RESISTANCE  OF  A   CELL 


213 


(of  the  same  diameter),  placed  together  in  the  circuit  so  that  the 
whole  current  passes  through  one  after  the  other ;  (c)  of  the 
smaller  high-resistance  wire ;  (d)  of  the  copper  wire.  In  each 
case  find  the  least  and  the  greatest  resistance  in  the  box  that  give 
the  correct  deflection,  but  record  only  their  average. 

Measure  (unless  given),  and  record  the  length  and  diameter  of 
each  wire. 

If  a  gravity  cell  is  provided  for  the  work,  leave  it  on  a  closed 
circuit  through  the  resistance  box,  with  the  2o-ohm  coil  in  the 
circuit.  (The  small  current  in  such  a  circuit  prevents  the  mixing 
of  the  two  liquids  by  diffusion.) 

Data.  —  Record  as  follows  :  — 


XlND    OF 

s  WIRE 

LENGTH  OF 
WIRE 

DIAMETER  OF 
WIRE 

DEFLECTION  OF 
GALVANOMETER 

RESISTANCE  OF 
WIRE 

a 











b 











c 











d 











Discussion.  —  i.  How  nearly  are  the  resistances  found  in  a  and 
b  proportional  to  the  lengths  of  the  wires  (considering  the  two 
wires  in  series  in  b  as  one  wire)  ? 

2.  How  nearly  are  the  resistances  found  in  a  and  c  inversely 
proportional  to  the  squares  of  the  diameters  of  the  wires? 

3.  Compute  the  ratio  of  the  resistance  of  the  high-resistance 
wire  to  the  resistance  of  an  equal  length  of  the  copper  wire  of  the 
same  diameter. 

EXERCISE   65.     THE   RESISTANCE   OF   A   CELL 

Principle  of  the  Method.  —  Let  C  (amperes)  denote  the  current 
which  an  electro- motive  force  E  (volts)  maintains  in  a  circuit 
whose  total  resistance  is  R  (ohms),  and  C  denote  the  current 


214 


ELECTRICITY 


which  the  same  electro-motive  force  maintains  in  a  circuit  whose 
resistance  is  R' ;  then,  by  Ohm's  Law, 

E  =  CR  =  C'R', 
from  which  we  have  the  proportion, 

C  :  C  : :  R1 :  R.     (E  constant.) 

That  is,  the  current  due  to  a  given  E.  M.  F.  is  inversely  pro- 
portional to  the  total  resistance  of  the  circuit  (including  the  resist- 
ance of  the  battery). 

In  the  following  experiment  a  constant  cell  (E  constant)  is 
connected  in  circuit  with  a  tangent  galvanometer  and  a  resistance 
box.  Let  r  denote  the  resistance  of  the  cell,  g  the  resistance  of 
the  galvanometer  coil,  and  R  and  R1  resistances  introduced  in 
the  box  at  different  times.  The  resistance  of  the  connecting 
wires  is  disregarded.  The  total  resistance  of  the  circuit  will  then 
be  r  -f-  g  -|-  R  in  the  first  case,  and  r  +  g  4-  R'  in  the  second. 
Letting  C  and  C'  denote  the  currents  maintained  through  these 
resistances  respectively,  the  above  proportion  becomes 

C :  C  :  :  (r  +  g  +  R')  :  (r  +  g  +  R). 

If  a  and  a'  denote  the  deflections  caused  by  the  currents  C  and 
C  respectively,  then 

C :  C  : :  tan  a  :  tan  a\     (Exercise  63.) 
From  these  two  proportions  we  have 

(r  +  g  +  R1)  :  (r  +  g  +  R)  :  :  tan  a  :  tan  a\ 

That  is,  with  a  constant  E.  M.  F.,  the  total  resistance  of  the 
circuit  is  inversely  proportional  to  the  tangent  of  the  angle  of 
deflection. 

Experiment  1 24.  —  To  find  the  resistance  of  a  constant  cell  by 
the  method  of  reduced  deflection. 

Apparatus.  —  A  tangent  galvanometer  of  low  resistance ;  con- 
stant cell  (gravity  or  Daniell) ;  resistance  box ;  commutator 
(useful  but  not  essential) ;  connecting  wires. 


THE   RESISTANCE  OF  A   CELL 


215 


Experimental  Work.  —  Adjust  the  galvanometer,  and  connect 
it  in  circuit  with  the  cell  and  the  resistance  box.  Include  the 
commutator  in  the  circuit,  if  one  is  provided.  Connect  with  the 
number  of  turns  of  the  galvanometer  that  gives  a  deflection 
nearest  to  50°  or  60°  when  no  resistance  is  introduced  in  the  box, 
and  use  only  this  connection  throughout  the  experiment. 

With  no  resistance  introduced  in  the  box  (R  =  o),  read  the 
position  of  both  ends  of  the  pointer  as  accurately  as  possible ;  re- 
verse the  current,  and  read  again.  The  average  of  these  four 
deflections  is  taken  as  the  true  deflection  a. 

Repeat  with  a  resistance  of  2  ohms  in  the  box  (R1  =  2),  and 
again  with  4  ohms  in  the  box  (R"  =  4). 

Record  the  resistance  of  the  number  of  turns  of  the  galvanom- 
eter used,  as  marked  on  the  instrument  or  given  by  the  teacher. 

Data  and  Computations.  — 

Resistance,  g,  of  the  number  of  turns  of  the 

galvanometer  coil  used  =       ohms. 


Box 
RESISTANCE 

DEFLECTION  OF  POINTER 

AVERAGE 
DEFLECTION 

TAN  a 

E.  end 

W.  end 

E.  end 

W.  end 

R     =o 

—  -N. 

S. 

-  o. 

N. 

a     =  



R'     =2 









a'    =  



R"  =4 









a"  =  



a.  Compute  the  resistance  r  of  the  cell  from  the  values  of  a,  a', 
R,  and  R\  substituting  in  the  proportion 

(r  +  g  +  R')i  (r+g+R)  : :  tan  a  :  tan  a'. 

b.  Compute  r  from  a,  a",  R,  and  R11. 

c.  Compute  r  from  a',  a",  R',  and  R". 

d.  With   careful  work  these    three   independently   determined 
values  of  r  should  differ  by  less  than  6  %.     Find  the  percentage 
of  difference  between  the  greatest  and  the  least  of  them. 


2I6  ELECTRICITY 

EXERCISE   66.     THE    ELECTRO-MOTIVE   FORCE   OF 
CELLS1 

References.  —  Adams,  495  ;  Coleman,  472-478 ;  Car.  &  C.,  465, 
478;  Ches.  G.  &T.,  390-392,404;  Mumper,  278-279,  285;  Jack- 
son, 106-107,  182  ;  Mil.  &  G.,  359-362  ;  Went.  &  H.,  292,  296. 

Experiment  125.  —  To  find  the  E.  M.  F.  of  cells  with  a  tangent 
galvanometer  having  a  high  resistance. 

Apparatus.  —  A  tangent  galvanometer  of  high  resistance  ;  grav- 
ity or  Daniell  cell ;  one  or  more  cells  for  the  measurement  of 
their  E.  M.  F. ;  commutator  (useful  but  not  essential). 

[The  galvanometer  must  have  a  resistance  of  at  least  100  ohms  ; 
200  ohms  or  more  is  better.  The  E.  M.  F.  of  the  gravity  or 
Daniell  cell  should  be  found  with  a  voltmeter  from  day  to  day, 
and  marked  on  the  cell.] 

The  Principle  of  the  Method.  — The  fall  of  potential  in  the  dif- 
ferent parts  of  a  circuit  (including  the  liquid  of  the  cell)  is  every- 
where proportional  to  the  resistance  of  the  different  parts.  For 
example,  if  the  resistance  of  the  cell  is  i  ohm  and  that  of  the  ex- 
ternal circuit  99  ohms,  the  fall  of  potential  in  the  liquid  of  the  cell 
from  the  zinc  to  the  carbon  plate  is  i  %  of  the  E.  M.  F.  of  the 
cell,  and  the  fall  of  potential  in  the  external  circuit  is  99  %  of  it. 
There  is,  therefore,  an  error  of  i  %  in  assuming  that  the  fall  of 
potential  in  the  external  circuit  is  equal  to  the  E.  M.  F.  of  the 
cell.  But  if  the  resistance  of  the  external  circuit  is  999  ohms, 
the  error  in  this  assumption  is  only  .1  %. 

It  will  be  seen  from  the  above  that,  if  the  coil  of  a  tangent  gal- 
vanometer has  a  resistance  of  at  least  two  or  three  hundred  ohms, 
the  potential  difference  between  its  terminals  when  connected 
with  a  cell  will  be  sensibly  equal  to  the  E.  M.  F.  of  the  cell,  and 
the  tangents  of  the  angles  of  deflection  will  be  proportional  to  this 

1  It  is  intended  that  only  one  of  the  experiments  of  this  exercise  be  taken, 
the  choice  depending  upon  the  laboratory  equipment. 


THE   ELECTRO-MOTIVE   FORCE   OF  CELLS 


E.  M.  F.  If  a  denotes  the  deflection  when  the  galvanometer  is 
connected  with  a  cell  whose  E.  M.  F.  is  E,  and  a1  the  deflection 
when  it  is  connected  with  a  cell  whose  E.  M.  F.  is  E1,  then1 

E  :  E[ :  :  tan  a  :  tan  a'.     (Resistance  constant.) 

Experimental  Work.  —  Adjust  the  galvanometer,  and  connect 
with  the  gravity  or  the  Daniell  cell.  Read  both  ends  of  the 
pointer,  reverse  the  current,  and  read  again.  Record  the  E.  M  F. 
of  the  cell,  as  marked  on  it  by  the  instructor. 

Connect  each  of  the  cells  in  turn  with  the  galvanometer,  and 
read  the  deflections  as  before. 

Data  and  Computations.  —  Compute  the  E.  M.  F.  of  each  cell 
from  the  formula 

£:E'::  tan  a  :  tan  a1, 

in  which  E  and  a  refer  to  the  gravity  or  the  Daniell  cell,  and 
E1  and  a?  to  each  of  the  other  cells  in  turn.  Record  as 
follows :  — 


DEFLECTION 

KIND  OF  CELL 

Av.  DEFLEC- 
TION a 

TAN  a 

E.  M.  F. 

E.  end 

W.  end 

Gravity 

N. 

s 

g 

N. 





(given) 

Leclanche 

N. 

g 

S. 

N. 







Etc. 







1  This  relation  does  not  hold  with  a  low-resistance  galvanometer,  for  in 
that  case  the  resistance  of  the  cells  would  be  a  large  part  of  the  whole  resist- 
ance of  the  circuit,  and  the  currents  (and  the  tangents  of  the  angles  of  deflec- 
tion) would  be  as  largely  affected  by  the  unequal  resistances  of  the  cells  as  by 
their  unequal  electro-motive  forces. 


2  1  8  ELECTRICITY 

Experiment  126.  —  To  find  the  E.  M.  F.  of  cells  by  the  method 
of  equal  deflections. 

Apparatus.  —  A  high-resistance  galvanometer  (not  necessarily 
a  tangent  instrument)  with  its  resistance  marked  on  it  ;  resistance 
box  ;  gravity  or  Daniell  cell,  with  its  E.  M.  F.  marked  on  it  ;  one 
or  more  cells  for  the  measurement  of  their  E.  M.  F. 

[Any  simple  galvanoscope  will  serve,  provided  it  has  a  sufficient 
number  of  turns  to  give  a  suitable  deflection  in  a  circuit  with  one 
cell  and  a  total  resistance  of  200  ohms  or  more.] 

Principle  of  the  Method.  —  Let  E  denote  the  E.  M.  F.  that 
maintains  a  current  C  in  a  circuit  whose  total  resistance  is  R,  and 
E'  the  E.  M.  F.  that  maintains  an  equal  current  through  a  total 
resistance  R'  ;  then,  by  Ohm's  Law, 


from  which  E  :  E1  :  :  R  :  R1.     (Current  constant.) 

That  is,  the  E.  M.  F.  necessary  to  maintain  a  given  current  is 
proportional  to  the  total  resistance  of  the  circuit. 

Experimental  Work.  —  Adjust  the  galvanometer  and  connect  it 
in  circuit  with  the  gravity  or  Daniell  cell  and  the  resistance  box  ; 
but  before  closing  the  circuit  introduce  a  high  resistance  in  the  box, 
to  avoid  possible  damage  to  the  galvanometer  by  too  large  a  cur- 
rent. Adjust  the  resistance  in  the  box  so  as  to  make  the  deflec- 
tion between  40°  and  50°,  and  read  one  end  of  the  pointer  as 
accurately  as  possible.  Record  the  deflection,  the  resistance  R 
introduced  in  the  box,  and  the  resistance  g  of  the  galvanometer 
coil.  If  R+g  is  greater  than  TOO  ohms,  the  resistance  of  the 
cell  may  be  disregarded  ;  but  its  approximate  value,  if  known, 
may  be  added  as  a  part  of  the  resistance  of  the  circuit. 

Substitute  each  of  the  cells  in  turn  for  the  one  just  used,  and 
repeat  the  above  work,  in  each  case  adjusting  the  resistance  R  in 
the  box  so  that  the  deflection  of  the  same  end  of  the  pointer  in 
the  same  direction  is  exactly  equal  to  the  first  deflection. 


THE   ELECTRO-MOTIVE   FORCE  OF  CELLS 


219 


Data  and  Computations.  —  Let  E  denote  the  known  E.  M.  F.  of 
the  gravity  cell  and  R  the  box  resistance  used  with  it,  £'  the  E.M.  F. 
of  any  one  of  the  other  cells,  and  R1  the  box  resistance  used  with 
it.  The  currents  were  equal  (how  do  we  know?)  ;  hence,  dis- 
regarding the  resistances  of  the  cells, 

E:E'::R+g:R!  +g.     (Why?) 

From  this  proportion  compute  the  E.  M.  F.  of  each  of  the  cells 
used.  Record  as  follows  :  — 


Deflection  for  each  adjustment      = 
Resistance  of  galvanometer  coil  g  = 


ohms. 


KIND  OF  CELL 

Box 

RESISTANCE  R 

R+g 

E.  M.  F. 

Gravity 

ohms 

ohms 

volts  (given) 

Etc. 







Experiment  127.  —  To  find  the  E.  M.  F.  of  cells  by  the  method 
of  reduced  deflection. 

Apparatus.  —  Galvanometer;  resistance  box;  gravity  or  Dan- 
iell  cell  with  its  E.  M.  F.  marked  on  it;  one  or  more  cells  for  the 
measurement  of  their  E.  M.  F. 

[Almost  any  galvanometer  will  serve,  of  either  low  or  high  re- 
sistance. A  tangent  galvanometer  with  a  15  -turn  coil  is  as 
good  as  any.  A  very  sensitive  galvanometer,  as  an  astatic  or  a 
D'Arsonval,  requires  the  use  of  a  shunt  or  of  very  high  resistances.] 

Principle  of  the  Method.  —  Let  C  denote  the  current  that  an 
E.  M.  F.  E  maintains  through  a  total  resistance  R,  and  Q  the 
current  when  the  resistance  is  increased  by  R±  ;  t.e. 


C=-  and  Ci± 
R 


220  ELECTRICITY 

Let  R*  denote  the  total  resistance  through  which  an  E.  M.  F. 
£'  maintains  the  first  current  C,  and  R±  the  added  resistance 
necessary  to  reduce  the  current  to  Ci ;  i.e. 


and 


Hence  C=     =      ' 


<p±.  P\     f 

(-"+-"1)       (f 
From  (i)  =      .  (3) 


From(2) 

Subtracting  the  members  of  (3)  from  the  corresponding  mem- 
bers of  (4)  we  have 

Ri  =  R£ 
E      E'9 

or  E  :  E1  :  :  ^  :  Rj. 

That  is,  the  two  electro-  motive  forces  are  proportional  to  the 
added  resistances  which  reduce  the  equal  currents  equally. 

Experimental  Work.  —  Adjust  the  galvanometer,  and  connect 
all  the  turns  of  its  coil  in  circuit  with  the  gravity  or  Daniell  cell 
and  the  resistance  box.  If  necessary,  introduce  resistance  in  the 
box  to  reduce  the  deflection  to  about  50°.  Read  one  end  of  the 
pointer  as  accurately  as  possible.  Record  the  deflection  and 
the  box  resistance.  Increase  the  box  resistance  till  the  deflection 
is  reduced  nearly  one  half.  Record  the  exact  deflection  and  the 
box  resistance. 

Substitute  each  of  the  cells  in  turn  for  the  one  just  used  ;  and 
in  each  case  adjust  the  box  resistance  so  as  to  give  first  and  sec- 
ond deflections  (of  the  same  end  of  the  pointer  in  the  same  direc- 
tion) exactly  equal  to  the  two  deflections  in  the  first  case. 
Record  the  box  resistances. 


ELECTRO-MOTIVE   FORCE   AND   RESISTANCE  OF  A  CELL     221 

Data  and  Computations.  —  Compute  the  E.  M.  F.  of  each  cell 
from  the  proportion 


in  which  E  denotes  the  E.  M.  F.  of  the  gravity  cell  and  £'  the 
E.  M.  F.  of  any  other  cell  used,  Rl  the  added  resistance  causing 
the  reduced  deflection  with  the  gravity  cell,  and  RJ  the  added 
resistance  with  the  other  cell.  The  resistances  of  the  galva- 
nometer and  of  the  different  cells  are  not  required.  Record  as 
follows  :  — 

First  deflection  (for  all  cells)      =       ° 
Second  deflection  (for  all  cells)  =       ° 


KIND  OF  CELL 

Box  RESISTANCE 

ADDED  RESIST- 
ANCE, Rl 

E.  M.  F. 

ISt 

2d 

Gravity 

ohms 

ohms 

ohms 

volts  (given) 

Etc. 









EXERCISE   67.     THE   ELECTRO-MOTIVE   FORCE   AND 
RESISTANCE   OF  A   CELL 

References.  —  Adams,  495-496  ;  Coleman,  472-478  ;  Car.  &  C., 
465,474,478;  Ches.  G.  &  T.,  390-392,  403-404;  Hoad.  Br., 
386,  39<>>  393-394;  Hoad.  EL,  430,  436;  Mumper,  273,  278- 
279,  285  ;  Jackson,  171,  175,  182;  Mil.  &  G.,  358-362,  369-370; 
Went.  &  H.,  292,  296. 

Experiment  128.  —  To  find  the  E.  M.  F.  and  the  resistance  of  a 
cell  by  means  of  a  voltmeter  and  an  ammeter. 

Apparatus. — Voltmeter;  ammeter;  cells  of  different  kinds; 
short  connecting  wires. 


222 


ELECTRICITY 


Experimental  Work.  —  Find  the  E.  M.  F.  of  a  cell  by  connect- 
ing its  poles  directly  to  the  voltmeter ;  then  connect  the  cell  with 
the  ammeter,  to  determine  the  current  that  the  cell  gives  when 
short-circuited  (the  resistance  of  the  ammeter  being  negligible). 
Repeat  with  each  of  the  cells  provided,  always  connecting  with 
the  voltmeter  first,  as  most  of  the  cells  will  begin  rapidly  to  polar- 
ize when  connected  with  the  ammeter,  thus  diminishing  their 
E.  M.  F. 

Data  and  Computations.  —  When  a  cell  is  connected  with  the 
ammeter,  the  external  resistance  may  be  disregarded,  with  very 
little  error;  i.e.  the  resistance  of  the  cell  may  be  taken  as  the 
whole  resistance  of  the  circuit.  Upon  this  assumption,  the  resist- 
ance of  the  cell  is  found  by  dividing  the  E.  M.  F.  of  the  cell  by 
the  reading  of  the  ammeter  (R=E  j  C).  Record  as  follows  :  — 


KIND  OF  CELL 

E.  M.  F.  OF  CELL 

CURRENT  THROUGH 
AMMETER 

RESISTANCE  OF 
CELL,  R  =  E/  C. 

volts 

amperes 

ohms 

EXERCISE   68.     FALL   OF   POTENTIAL  ALONG  A 
CONDUCTOR 

References.  —  Adams,  497;  Coleman,  475-478;  Car.  &  C., 
478  ;  Ches.  G.  &  T.,  390-392,  404  ;  Hoad.  Br.,  386,  394  ;  Hoad. 
El.,  430,  433  ;  Mumper,  285  ;  Jackson,  106-107,  171,  175,  182  ; 
Mil.  &  G.,  359-362  ;  Went.  &  H.,  292,  296. 

Experiment  129.  —  To  study  the  relation  between  the  fall  of 
potential  in  the  different  parts  of  a  circuit  and  the  resistances  of 
those  parts. 


FALL   OF   POTENTIAL   ALONG  A   CONDUCTOR 


223 


Apparatus.  —  Tangent  galvanometer  of  high  resistance,  or  volt- 
meter ;  board  with  stretched  wires  ;  one  or  more  cells,  as  needed ; 
connecting  wires. 

[The  directions  for  the  experiment  are  adapted  to  the  tangent 
galvanometer.  A  voltmeter  simplifies  the  work,  but  the  smallest 
divisions  of  the  scale  must  not  be  greater  than  .  i  volt.  A  d'Ar- 
sonval  galvanometer  may  be  used,  if  provided  with  a  suitable 
shunt  to  reduce  the  deflections.  Three  German  silver  wires, — 
two  of  No.  26  and  one  of  No.  30,  —  each  stretched  between 
binding  posts  i  m.  apart,  and  15  m.  of  No.  30  insulated  copper 
wire,  also  connected  with  a  pair  of  binding  posts  (Fig.  101),  are 

1 


U  

o 

o 

FIG.  101. 


suitable  for  this  experiment  and  also  for  Experiment  123.  The 
No.  30  German  silver  wire  must  be  bare,  and  should  be  stretched 
over  a  meter  stick,  for  convenience  in  measuring  off  lengths.  The 
distances  between  the  binding  posts  can  be  reduced  to  50  cm. 
by  using  wire  having  a  specific  resistance  of  40  to  50  instead  of 
German  silver ;  and  with  such  wire  somewhat  larger  sizes  can  be 
used,  giving  greater  durability.  It  is  only  necessary  that  the  resist- 
ances of  the  wires  be  large  enough  to  give  good  results  (2  to  5 
ohms  each),  and  that  the  copper  wire  be  of  the  same  diameter  as 
one  of  the  others.] 

Experimental  Work.  —  a.  Connect  the  cell  (or  two  or  more 
cells  in  series)  with  the  binding  posts  a  and  b  (Fig.  101),  between 
which  the  smaller  high-resistance  wire  is  stretched.  Connect  one 


224 


ELECTRICITY 


terminal  of  the  high-resistance  coil  of  the  galvanometer  (or  the 
voltmeter)  with  the  post  a.  Connect  a  short  wire  with  the  other 
terminal  of  the  galvanometer,  and  press  the  other  end  of  this  wire 
firmly  down  upon  the  stretched  wire  exactly  25  cm.  from  a. 
Read  the  deflection  indicated  by  both  ends  of  the  pointer.  Re- 
peat, taking  the  point  of  contact  c  50  cm.,  75  cm.,  and  100  cm. 
from  a.  (If  the  length  of  the  wire  is  50  cm.,  reduce  each  of  these 
distances  one  half.) 

Reverse  the  connections  with  the  galvanometer,  so  that  the 
deflections  will  be  in  the  opposite  direction,  and  repeat  the  read- 
ings for  each  of  the  above  adjustments.  The  average  of  the  four 


^n  

-n— 

readings  for  each  adjustment  is  taken  as  the  true  deflection.  If  a 
voltmeter  is  used,  a  single  reading  for  each  adjustment  is  all  that 
is  required. 

b.  Connect  the  battery  in  series  with  the  stretched  copper 
wire,  one  of  the  larger  high-resistance  wires,  and  the  smaller  high- 
resistance  wire,  as  shown  in  Figure  102,  using  short  connecting 
wires  between  the  posts.  Find  the  deflection  of  the  galvanometer 
when  connected  with  the  binding  posts  at  the  ends  of  the  smaller 
high-resistance  wire  (see  figure).  Reverse  the  current  through 
the  galvanometer,  and  take  the  average  of  the  four  readings  as 
the  true  deflection. 


FALL  OF   POTENTIAL  ALONG  A  CONDUCTOR  225 


In  the  same  way  find  the  deflection  of  the  galvanometer  when 
connected  with  the  ends  of  the  larger  high-resistance  wire  (mak- 
ing no  change  in  the  main  circuit),  and  when  connected  with  the 
ends  of  the  copper  wire. 

Record  the  lengths  and  diameters  of  the  different  wires. 

Data  and  Computations.  —  Let  /denote  the  length  of  stretched 
wire  between  the  terminals  of  the  galvanometer  in  Part  a  of  the 
experiment.  Record  as  follows  :  — 

PART  a 


DEFLECTION 

I 

Av.  DEFLEC- 
TION a 

TAN  a 

/-T-TAN  a 

E.  end 

W.  end 

25  cm. 

N. 

S. 

CJ 

"NT 

50  cm. 

N. 

S. 

S. 

-N. 







75  cm. 

N. 

S. 

S. 

N. 



• 



100  cm. 

JsJ 

S. 

S. 







PART  b 


STRETCHED  WIRE  BETWEEN 
GALVANOMETER  TERMINALS 

DEFLECTION 

Av.  DEFLEC- 
TION a 

TAN* 

Kind 

Length 

Diameter 

E.  end 

W.  end 



cm. 

cm. 

—  N. 

S. 

S. 

N. 

—  — 









N. 

S. 

S. 

N. 



,  

Copper 





N. 

S. 

S. 

N. 



COLEMAN'S  NEW  MANUAL — 15 


226  ELECTRICITY 

Discussion. —  i.  The  resistance  of  any  portion  of  the  stretched 
wire  is  proportional  to  its  length ;  the  fall  of  potential  in  any 
portion  is  proportional  to  its  resistance  (Ohm's  Law  as  applied  to 
the  parts  of  a  circuit)  ;  and  the  potential  difference  between  the 
terminals  of  the  galvanometer  (i.e.  the  fall  of  potential  in  the  part 
of  the  stretched  wire  between  these  terminals)  is  proportional  to 
the  tangent  of  the  angle  of  deflection  (why?)  ;  hence  the  lengths 
of  the  parts  of  the  stretched  wire  between  the  terminals  of  the 
galvanometer  in  Part  a  should  be  proportional  to  the  tangents  of 
the  angles  of  deflection  (i.e.  the  quotient  /-=-  tan  a  should  be  con- 
stant). Within  what  percentage  of  difference  do  you  find  this 
relation  to  hold? 

2.  Do  the  deflections  of  the  galvanometer  indicate  equal  or 
unequal  fall  of  potential  in  the  whole  length  of  the  smaller  high- 
resistance  wire  in  Parts  a  and  bl     How  do  you  account  for  this? 

3.  From  the  measured  diameters   of  the   two   high-resistance 
wires,  compute    the  ratio    of  the    resistances  of   i   m.  of  each. 
Compute  the  ratio  of  the  fall  of  potential  in  one  to  the  fall  of 
potential  in  the  other  in  Part  b  (given  by  the  ratio  of  the  tangents 
df  the  deflections).     How  should  these  ratios  compare,  and  why? 
Is  the  fall  of  potential  more  or  less  rapid  in  the  larger  wire  than 
in  the  smaller?     Why? 

4.  Assuming  Ohm's  Law,  find,  from  the  data  obtained  in  Part  b 
with  the  copper  wire  and  the  high-resistance  wire  of  the  same 
diameter,  the  ratio  of  the  resistance  of  the  latter  to  the  resistance 
of  an  equal  length  of  the  copper  wire.     This  ratio  is  the  specific 
resistance  of  the  high-resistance  wire  referred  to  copper. 

EXERCISE  69.     MEASUREMENT  OF  RESISTANCE  WITH 
THE   WHEATSTONE   BRIDGE 

References :  The  Wheatstone  Bridge 

Adams,  498;  Car.  &  C.,  476-479;  Ches.  G.  &  T.,  412; 
Hoad.  Br.,  389;  Hoad.  EL,  434;  Mumper,  284-286;  Jackson, 
106,  162-168;  Went.  &  H.,  291-293. 


THE   WHEATSTONE   BRIDGE  227 

The  d'Arsonval  Galvanometer 

Adams,  490;  Coleman,  484;  Car.  &  C.,  473;  Ches.  G.  &  T., 
405  ;  Hoad.  Br.,  385  ;  Hoad.  EL,  429  ;  Mumper,  261 ;  Jackson^ 
151-152;  Mil.  &  G.,  356;  Went.  &  H.,  280. 

The  Astatic  Galvanometer 

Coleman,  483  ;  Hoad.  Br.,  383  ;  Hoad.  EL,  427  ;  Jackson,  149; 
Went.  &  H.,  280. 

Principle  of  the  Bridge.  —When  two  points,  A  and  B  (Fig.  103), 
on  an  electric  circuit  are  connected  by  two  branches,  as  AMB  and 
ANB,  the  fall  of  potential 
is  the  same  in  both  branches,  Jv; 

since  in  both  it  is  the  po-        A^/^  ^/)  "^^-5. 

tential  difference  between 
the  points  A  and  B.  Let 
N  be  the  point  in  one 
branch  whose  potential  is 
the  same  as  that  of  a  given 
point  M  in  the  other 
branch.  Then  the  fall  of 

potential  in  AM  is  equal  to  that  in  AN,  and  the  fall  in  MB 
is  equal  to  that  in  NB.  But,  by  Ohm's  Law,  the  fall  of  potential 
in  AM  is  to  that  in  MB  as  the  resistance  of  AM,  or  rl9  is  to 
the  resistance  of  MB,  or  r2 :  and  similarly  in  the  other  branch. 
Hence  r±  :  r2  :  :  rs  :  r4.  If  any  three  of  these  resistances  are 
known,  the  fourth  can  be  computed  from  this  proportion. 

The  equipotential  points  M  and  TV  are  found  experimentally  by 
means  of  a  sensitive  galvanometer  placed  in  the  "  bridge  "  joining 
the  two  branches.  The  resistances  are  varied  (as  described  below) 
till  the  deflection  of  the  galvanometer  is  zero.  We  then  know 
that  there  is  no  current  through  the  wire  joining  M  and  N,  and 
consequently  that  these  points  are  at  equal  potentials.  The  two 
branches  of  the  divided  battery  circuit  AMB  and  ANB,  together 


228 


ELECTRICITY 


with  the  cross  branch  MN9  constitute  a  Wheatstone  bridge.  The 
parts  AM,  MB,  AN,  and  NB  are  the  four  arms  of  the  bridge. 
The  Wheatstone  bridge  is  made  in  various  forms,  but  the  above 
statement  of  the  principle  holds  for  all. 

The  Slide  Wire  Bridge.  —  This  form  of  the  Wheatstone  bridge 
(Figs.  104  and  105)  derives  its  name  from  a  stretched  bare  wire, 


FIG.  104. 

the  parts  of  which,  4  and  L2,  constitute  two  arms  of  the  bridge. 
The  resistance  to  be  measured  (^  in  the  figure)  is  placed  in 
either  of  the  arms  AM  or  MB,  and  a  resistance  box  is  placed  in 
the  other.  The  resistance  of  the  large  brass  connecting  bars 
in  these  arms  is,  of  course,  negligible.  The  battery  terminals  are 


/3W&wflp*r\ 


FIG.  105. 

connected  to  posts  at  A  and  B.  One  terminal  of  the  galvanom- 
eter is  connected  with  a  post  at  M,  and  the  other  is  brought  in 
contact  with  any  desired  point  of  the  stretched  wire  by  means  of 
the  sliding  contact  key  N. 


THE   WHEATSTONE  BRIDGE  22Q 

When  the  position  of  the  key  ^V  is  such  that  there  is  no  deflec- 
tion of  the  galvanometer  on  closing  the  circuit  through  it,  the 
resistances  of  the  segments  /j.  and  /2  into  which  the  wire  is  divided 
by  the  point  of  contact  of  the  key  are  in  the  same  ratio  as  ^  and 
r2 ;  or,  since  the  lengths  /x  and  /2  are  in  the  same  ratio  as  their 
resistances,  /x :  /2 :  :  ^  :  r%.  Hence  if  rv  is  the  unknown  resistance, 
it  is  computed  from  the  equation  r±  =  /i^2/4- 

The  lengths  /x  and  /2  can  be  more  accurately  determined  when 
neither  is  small ;  it  is  therefore  best  to  have  them  nearly  equal. 
This  requires  that  the  box  resistance  be  nearly  equal  to  the 
resistance  to  be  measured.  Hence  in  measuring  a  resistance, 
begin  by  introducing  in  the  box  a  resistance  estimated  to  be 
somewhere  nearly  equal  to  it.  With  the  battery  circuit  closed, 
touch  the  slide  wire  with  the  contact  key  near  one  end,  and  note 
the  direction  of  the  deflection.  Slide  the  key  to  about  an  equal 
distance  from  the  other  end,  and  repeat.  (Do  not  slide  the  key 
when  closed :  the  wire  would  be  damaged  by  scraping  it.)  If  the 
deflection  is  in  the  same  direction  a's  before,  the  resistance  in  the 
box  is  much  too  large  or  too  small.  If  you  are  doubtful  which  is 
the  case,  make  contact  nearer  either  or  both  ends,  till  an  oppo- 
site deflection  is  obtained.  Having  properly  adjusted  the  box 
resistance,  and  having  found  two  points  between  which  the  cor- 
rect point  of  adjustment  lies  (the  two  points  giving  deflections 
in  opposite  directions),  the  adjustment  is  completed  by  noting  the 
decreasing  deflection  of  the  galvanometer  in  either  direction  as 
the  points  of  contact  are  taken  at  diminishing  distances  on  each 
side  of  the  point  sought.  With  a  sensitive  d'Arsonval  galvanom- 
eter, the  adjustment  should  be  right  within  i  mm. 

The  Resistance-coil  Bridge.  —  In  each  of  the  arms  AM  and  AN 
of  this  form  of  bridge  a  resistance  coil  (i,  10,  or  100  ohms)  is 
introduced  by  removing  a  plug,  as  in  a  resistance  box.  The  re- 
sistance of  the  brass  connecting  bars  is  negligible.  The  resist- 
ance to  be  measured  (;2  in  the  figure)  is  placed  in  either  of  the 
arms  ME  or  NB,  and  a  resistance  box  r±  (in  the  figure)  is  placed 


230 


ELECTRICITY 


in  the  other.     The  box  resistance  is  adjusted  to  give  a  zero  deflec- 
tion of  the  galvanometer. 

The  results  are  most  accurate  when  the  coil  used  for  r^  is  the 
one  most  nearly  equal  to  r>2  and  when  the  ratio  r^/r^  is  so  taken 

that  ?\  is  not  far  from 
the  full  capacity  of  the 
box.  It  is  generally 
better  to  begin  with 
equal  values  for  ^  and 
>  B  r3,  and  to  change  the 
ratio  later  if  this  is 
found  to  be  desirable. 
The  circuit  through  the 
galvanometer  is  mo- 
mentarily closed,  by 
means  of  the  contact 
key,  after  each  adjust- 
ment of  the  resistance.  The  battery  circuit  may  be  kept  closed ; 
but  if  a  key  is  provided  for  this  circuit,  it  is  closed  before  and 
opened  after  the  galvanometer  circuit. 

In  measuring  a  resistance,  note  first  the  direction  of  the  deflec- 
tion when  the  box  resistance  is  zero  ;  then  introduce  a  resistance 
estimated  to  be  about  equal  to  the  one  you  are  measuring.  If 
the  deflection  is  in  the  same  direction  as  before,  introduce  more 
resistance ;  if  it  is  in  the  opposite  direction,  replace  the  plug 
firmly  and  introduce  a  smaller  resistance.  Proceed  thus  down 
to  the  smallest  resistance  in  the  box,  or  until  there  is  no  deflec- 
tion. When  the  correct  adjustment  is  secured,  rs  is  found  from 
the  equation  r2  =  ; 


FIG.  106. 


Experiment  130.  —  To  measure  electrical  resistance  by  means  of 
a  Wheatstone  bridge. 

Apparatus.  —  A  Wheatstone  bridge  ;  d'Arsonval  or  astatic  gal- 
vanometer ;  dry  (or  other)  cell ;  resistance  box  ;  resistance  to  be 
measured ;  connecting  wires. 


THE   WHEATSTONE  BRIDGE 


231 


[The  slide  wire  bridge  is  recommended  unless  the  laboratory 
is  already  supplied  with  the  other  form.  A  satisfactory  d'Arson- 
val  galvanometer,  similar  to  Figure 
107,  very  sensitive,  suitable  for  use 
with  the  bridge  and  for  experiments 
on  induced  currents,  can  be  bought 
for  $7.00  to  $12.00.  These  are 
dead-beat  instruments,  which  is  a 
very  important  advantage  over  the 
astatic  type.] 

Experimental  Work.  —  In  measur- 
ing any  resistance  with  a  Wheatstone 
bridge,  follow  the  directions  given 
above.  Find  the  resistance  of  such 
of  the  following  conductors  as  are 
provided  :  — 

1.  The  filaments  of  incandescent 

lamps;  e.g.    a   i6-candle,    no-volt   lamp;  a  32-candle,   no-volt 
lamp;  a  i6-candle,  22O-volt  lamp;  a  32-candle,  22O-volt  lamp. 

2.  Coils  of  electro-magnets ;  e.g.  of  a  telegraph  sounder,  tele- 
graph relay,  electric  bell,  and  the  armature  of  a  motor  or  dynamo. 

3.  The  coil  of  a  galvanometer  or  a  voltmeter. 
Experiment  131.  —  To  measure  the  resistance  of  a  cell. 
Apparatus.  —  As   for  Experiment   130;   also  two  of  the  cells 

whose  resistance  is  to  be  found. 

Experimental  Work.  —  The  two  cells  whose  resistance  is  to  be 
determined  must  be  of  the  same  kind  and,  as  nearly  as  possible, 
in  the  same  condition,  in  order  that  their  electro-motive  forces 
may  be  equal.  Place  them,  connected  in  series  and  opposing  each 
other,  in  one  arm  of  the  bridge.  When  thus  connected  their 
combined  E.  M.  F.  is  zero,  and  their  effect  in  the  bridge  is  that 
of  a  simple  resistance  equal  to  the  sum  of  their  separate  resist- 
ances. A  third  cell  must,  of  course,  be  used  in  the  usual  manner 
to  supply  a  current  to  the  bridge. 


232  ELECTRICITY 

Experiment  132.  —  To  find  the  relative  resistance  of  different 
metals,  referred  to  copper. 

Apparatus.  —  As  for  Experiment  130;  also  copper  and  other 
wires  of  the  same  diameter  and  any  convenient  lengths. 

Experimental  Work.  —  Find  and  record  the  length,  diameter, 
and  resistance  of  each  wire.  Compute  the  ratio  of  the  resistance 
of  each  wire  to  the  resistance  of  a  copper  wire  of  the  same  length 
and  diameter.  Compare  the  values  obtained  with  the  values 
given  in  tables.  Enter  data  and  computations  in  tabular  form. 

Experiment  133. —  To  study  the  relation  between  the  resistance 
of  a  wire  and  its  cross  section. 

Apparatus.  —  As  for  Experiment  130;  also  two  or  more  wires 
of  the  same  material  and  length,  but  of  different  diameters ;  mi- 
crometer screw  (unless  the  diameters  of  the  wires  are  given). 

Experimental  Work.  —  Find  the  lengths,  diameters,  and  resist- 
ances of  the  different  wires.  Find  within  what  percentage  of  error 
the  measured  resistances  and  diameters  agree  with  the  known  law. 
Enter  data  and  computations  in  tabular  form. 

EXERCISE    70.     ARRANGEMENT   OF   CELLS 

References.  —  Adams,  499-504  ;  Coleman,  477,  479-482  ;  Car. 
&C.,  467-470;  Ches.  G.  &  T,  396-399 ;  Hoad.  Br.,  358-362  ; 
Hoad.  El.,  401-405;  Mumper,  283;  Jackson,  38;  Mil.  &  G., 
384-386;  Went.  &  H.,  297. 

Experiment  134. —  To  study  the  arrangement  of  cells  in  series 
and  in  parallel;  and  to  find  which  arrangement  gives  the  larger 
current  through  a  given  external  resistance. 

Apparatus.  —  Tangent  galvanometer  of  low  resistance  and  one 
of  high  resistance  (the  latter  can  be  dispensed  with),  or  a  volt- 
meter and  an  ammeter ;  two  cells  of  the  same  kind ;  resistance 
box  ;  double  connectors  ;  connecting  wires. 

[The  cells  should  be  of  the  same  size  and  as  nearly  as  possible 


ARRANGEMENT   OF   CELLS 


233 


FIG.  108. 


in  the  same  condition,  in  order  that  they  may  have  equal  E.  M.  F. 
and  approximately  equal  resistance.  The  resistance  of  good  dry 
cells  is  so  small  that  they  fail  to  show  the  advantage  of  connec- 
tion in  parallel,  unless  the  whole  external  resistance  is  only  a  few 
hundredths  of  an  ohm). 

Experimental  Work.  —  Find  the  ratio  of  the  E.  M.  F.  of  a  bat- 
tery of  two  like  cells  in  series 
(Fig.  108)  to  that  of  one  cell,  and 
the  ratio  of  the  E.  M.  F.  of  the 
two  cells  in  parallel  (Fig.  109)  to 
that  of  one  cell.  If  a  tangent 
galvanometer  of  high  resistance  is 
provided  for  this  purpose,  follow 
the  method  of  Experiment  125  and  the  form  of  record  given 
below  ;  with  a  high-resistance  galvanometer,  which  is  not  a  tangent 
instrument,  follow  the  method  of^Experiment 
126;  with  a  low-resistance  galvanometer,  follow 
the  method  of  Experiment  127;  with  a  volt- 
meter, measure  directly  the  E.  M.  F.  of  each  cell 
separately,  of  both  in  series,  and  of  both  in 
parallel,  as  in  Experiment  128. 

Connect  the  low-resistance  galvanometer  (or 
the  ammeter)  in  circuit  with  the  resistance  box 
and  one  cell.  Use  the  number  of  turns  of  the 
coil  which  gives  a  deflection  nearest  to  45°  with 
no  box  resistance ;  and  use  the  same  connection 
in  all  that  follows.  Read  to  the  nearest  degree  the  deflection 
(of  one  end  of  the  pointer  in  one  direction)  with  a  box  resistance 
R  of  o  ohms  ;  with  R  =  3  ohms  ;  and  with  R=2O  ohms.  Repeat 
with  a  battery  of  two  cells  in  series  and  the  same  box  resistances. 
Read  the  same  end  of  the  pointer  as  before,  with  the  deflection 
in  the  same  direction.  Repeat  with  a  battery  of  two  cells  in  paral- 
lel and  the  same  box  resistances.  Record  as  indicated  below.  If 
an  ammeter  is  used,  all  the  readings  will  be  in  amperes. 


234 


ELECTRICITY 


Data  and  Computations.  —  Make  diagrams  of  the  series  and 
parallel  arrangements,  representing  the  resistance  box  and  the 
galvanometer  in  the  circuit.  With  a  tangent  galvanometer  of 
high  resistance  and  a  low-resistance  instrument  (tangent  or  other), 
record  as  follows  :  — 


E.  M.  F.  OF  TWO   CELLS    IN  SERIES   AND    IN  PARALLEL   COMPARED   WITH   THAT 
OF  A  SINGLE  CELL.       (HiGH-RESISTANCE  GALVANOMETER.) 


NO.  AND 

ARRANGEMENT 
OF  CELLS 

DEFLECTION 

Av.  DEFLECTION 

TANGENT 

RATIO  OF 
ELECTRO- 
MOTIVE 
FORCES 

E.  end 

W.  end 

I 

N. 

;  o 

S. 

N. 



tan  a 

2,  in  series 

N. 

S. 

S. 

N. 



tan  a- 

tan  af  -Man  a 

2,  in  parallel 

*—  N. 

S. 

S. 

N. 



tan  a" 

tan  a'1  -4-  tan  a 

CURRENT  FROM  TWO  CELLS  IN  SERIES  AND  IN  PARALLEL  COMPARED  WITH 
THAT  FROM  SINGLE  CELL.     (LOW-RESISTANCE  GALVANOMETER.) 


No.  AND  ARRANGE- 
MENT OF  CELLS 

DEFLECTION  WITH  Box  RESISTANCE  R 

ARRANGEMENT 
GIVING  THE 
LARGER  CURRENT 

R=o  ohms 

R=3  ohms 

K  =  2o  ohms 

I 

2,  in  series 
2,  in  parallel 









Discussion. —  i.  How  does  the  E.  M.  F.  of  the  two  cells  in 
series  compare  with  that  of  one  cell?  the  E.  M.  F.  of  the  two 
cells  in  parallel? 


MEASUREMENT   OF   ELECTRICAL   POWER  235 

2.  From  the  known  law  of  resistances  in  series  and  in  parallel 
(which  holds  for  cells  as  well  as  for  other  conductors),  how  does 
the  resistance  of  a  battery  of  two  like  cells  in  series  compare  with 
that  of  one  cell?  the  resistance  of  a  battery  of  two  like  cells  in 
parallel  ? 

3.  Letting  E  denote  the  E.  M.  F.  and  r  the  resistance  of  one 
cell,  R  the  external   resistance,   and    C  the   current,  write   the 
formula  for  the   current  from  a  battery  of  two  cells  in  series ; 
also  the  formula  for  the  current  from  a  battery  of  two  like  cells 
in  parallel. 

4.  Show  from  the  results  of  the  experiment  which  arrangement 
of  cells  gives  the  larger  current  through  a  very  low  external  re- 
sistance (R  =  o)  ;  and  which  arrangement  gives  the  larger  current 
through  a  considerable  external  resistance  (R  =  20). 

5.  Account  for  these  results  by  means  of  the  formulas  given  in 
answer  to  the  third  question. 

EXERCISE   71.     MEASUREMENT   OF   ELECTRICAL 
POWER 

References.  — Adams,  541-544  ;  Coleman,  486-491 ;  Ches.  G. 
&  T.,  387  ;  Hoad.  Br.,  395  ;  Hoad.  El.,  437  ;  Mumper,  280-281 ; 
Jackson,  no,  112-113,  331;  Mil.  &  G.,  404-407;  Went.  &  H., 
299-302. 

Electrical  Power.  —  The  unit  of  electrical  power  is  the  energy 
expended  per  second  by  a  current  of  i  ampere  in  any  part  of 
the  circuit  in  which  the  fall  of  potential  is  i  volt.  This  unit  is 
called  the  watt.  The  power  of  an  electric  current,  or  the  total 
energy  expended  by  it  in  the  entire  circuit  in  one  second,  meas- 
ured in  watts,  is  equal  to  the  product  of  the  E.  M.  F.  and  the 
current;  i.e.  P=  EC  watts,  in  which  P  denotes  the  electrical 
power,  E  the  E.  M.  F.  in  volts,  and  C  the  current  in  amperes. 

The  power  used  in  any  part  of  a  circuit  is  measured  in  watts 
by  the  product  of  the  current  and  the  fall  of  potential  in  that 


ELECTRICITY 


part  of  the  circuit.  For  example,  if  a  i6-candle  lamp  takes  a 
current  of  .5  ampere  and  the  potential  difference  between  its 
terminals  is  no  volts,  the  power  expended  in  it  is  .5  x  no,  or 
55  watts.  This  is  3.44  watts  per  candle  power  (55  -r-  16  =  3.44). 

Experiment  135.  —  To  measure  the  power  generated  by  a  battery 
when  lighting  an  incandescent  lamp  ;  and  to  determine  the  percent- 
age of  the  total  power  consumed  in  the  battery  and  in  the  lamp. 

Apparatus.  —  A  small  incandescent  lamp;  a  sufficient  number 
of  cells  to  light  the  lamp ;  voltmeter ;  ammeter ;  two  double 
connectors  ;  connecting  wires. 

[Dry  cells  are  best  and  most  convenient.  Lamps  requiring 
from  two  to  four  dry  cells  in  series  are  suitable.  If  the  laboratory 
is  not  provided  with  such  lamps,  the  coil  of  an  electro-magnet  or 
any  resistance  coil  may  be  used  instead.] 

Experimental  Work.  —  Connect  the  lamp  and  the  ammeter  in 
circuit  with  one  cell.  If  the  current  is  not  sufficient  to  light  the 
lamp,  add  a  second  cell  in  series  with  the  first,  and,  if  necessary, 

a  third  and  a  fourth  cell. 
Use  only  a  sufficient  num- 
ber of  cells  to  light  the 
lamp  brightly ;  if  too 
many  are  used,  the  fila- 
ment will  be  burned  out 
and  the  lamp  destroyed. 

Connect  the  voltmeter 
as  a  shunt  to  the  lamp 
A  (V,  Fig.  no)  to  deter- 
mine the  potential  differ- 
ence between  its  termi- 
nals. Read  the  ammeter  and  the  voltmeter.  Do  not  keep  the 
circuit  closed  longer  than  is  necessary.  Make  a  diagram  of  the 
circuit. 

Find  the  E.  M.  F.  of  the  battery  by  connecting  its  terminals 


FIG.  no. 


MEASUREMENT   OF   ELECTRICAL   POWER  237 

directly  to  the  voltmeter  (the  lamp  and  the  ammeter  being  re- 
moved from  the  circuit). 

Record  the  candle  power  of  the  lamp. 

Data  and  Computations.  —  Let  Pt  denote  the  fall  of  potential  in 
the  lamp  and  Pb  the  fall  or  loss  of  potential  in  the  battery,  when 
on  the  lamp  circuit.  (The  loss  of  potential  in  the  battery  is  practi- 
cally zero  when  connected  directly  with  the  voltmeter,  as  explained 
in  Experiment  125.)  Hence,  letting  E  denote  the  E.  M.  F.  of 
the  battery,  and  assuming  the  loss  of  potential  in  the  ammeter  and 
the  connecting  wires  to  be  negligible,  E  =  Pb  -f  Pl  (i.e.  the  total 
fall  of  potential  in  the  whole  circuit  is  equal  to  the  E.  M.  F.  of  the 
battery). 

If  the  current  through  the  lamp  circuit  is  denoted  by  C,  the 
total  power  generated  by  the  battery  when  on  the  lamp  circuit  is 
EC  watts,  the  power  expended  in  the  lamp  is  PtC,  and  the  power 
lost  in  the  battery,  due  to  internal  resistance,  is  PbC. 

Record  data  as  follows,  and  perform  the  indicated  computa- 
tions :  — 

Current  supplied  to  the  lamp  C  =  amperes. 

Potential  difference  between  the  lamp  terminals  Pl  =  volts. 

E.  M.  F.  of  battery  E  =  volts. 

Candle  power  of  the  lamp  = 

Loss  of  potential  in  the  battery  when  on  the  lamp 

circuit  Pb  =  E-Pl  =  volts. 

Total  power  generated  by  the  battery  when  on  the 

lamp  circuit  EC  =  watts. 

Power  expended  in  the  lamp  PtC  =  watts. 

Power  lost  in  the  battery  PbC  =  watts. 

Percentage  of  total  power  utilized  in  the  lamp          =  % 

Percentage  of  total  power  lost  in  the  battery  =  % 

Discussion.  — i.  By  Ohm's  Law,  the  losses  of  potential  in  the 
battery  and  in  the  lamp  are  proportional  to  their  respective  resist- 
ances, and  the  total  resistance  is  E/  C.  From  this  compute  the 


238  ELECTRICITY 

resistance  of  the  battery  and  the  resistance  of  the  lamp.     (Since 
Pb,  as  found,  really  includes  the  loss  of  potential  in  the  ammeter 
and  the  connecting  wires,  the   computed   battery  resistance  will 
include  the  resistance  of  the  ammeter  and  the  connecting  wires.) 
2.    Compute  the  watts  per  candle  power  consumed  by  the  lamp. 


EXERCISE    72.     INDUCED    CURRENTS 

References.  — Adams,  505-512,  524  ;  Coleman,  492-495  ;  Car. 
&  C.,  480-482  ;  dies.  G.  &  T.,  415-422  ;  Hoad.  Br.,  397  ;  Hoad. 
EL,  439-440;  Mumper,  287-291;  Jackson,  132-137;  Mil.  &  G., 
412-417  ;  Went.  &  H.,  313-315- 

Apparatus.  —  A  d'Arsonval  or  astatic  galvanometer  ;  induction 
coil  with  movable  primary  and  iron  core  ;  dry  cell ;  bar  magnet ; 
connecting  wires. 

[The  usual  form  of  separable  induction  coil,  in  which  the  sec- 
ondary coil  consists  of  many  turns  of  fine  wire,  requires  a  d'Arson- 
val or  an  astatic  galvanometer  of  fairly  high  resistance.  With  an 
astatic  galvanometer  of  low  resistance,  the  secondary  coil  should 
consist  of  a  few  turns  of  large  wire,  like  the  primary.] 

Experiment  136. —  To  study  the  laws  of  current  induction  by 
magnets. 

Experimental  Work.  —  a.  Since  the  galvanometer  is  to  be 
used  to  determine  the  direction  as  well  as  the  existence  of  induced 
currents,  it  is  first  necessary  to  observe  the  direction  of  the  de- 
flection due  to  a  current  whose  direction  is  known.  Use  the  cell 
for  this  purpose  ;  but  before  closing  the  circuit,  connect  the  termi- 
nals of  the  galvanometer  with  a  short  wire,  which  will  act  as  a 
shunt  to  the  galvanometer,  permitting  only  a  small  fraction  of  the 
current  to  pass  through  it.  (This  is  a  necessary  precaution  with 
a  sensitive  instrument.)  Observe  the  direction  of  the  deflection, 
and  note  (from  the  battery  connections)  by  which  terminal  the 


INDUCED    CURRENTS 


239 


current  enters  the  galvanometer.  A  current  entering  by  the  other 
terminal  would  cause  a  deflection  in  the  opposite  direction. 
Hence  in  the  following  experiments  the  direction  of  the  deflection 
will  indicate  by  which  terminal  the  current  enters  the  galvanom- 
eter ;  and  from  this  the  direction  of  the  current  can  be  traced 
through  the  entire  circuit. 

b.  Connect  the  galvanometer  with  the  larger  coil  of  wire  (called 
the  secondary  coil),  placed  at  a  distance  of  a  meter  or  more. 
The  circuit  consists  only  of  the  coil,  the  galvanometer,  and  the 
connecting  wires. 

Thrust  the  north  pole  of  the  magnet  suddenly  into  the  coil, 
while  observing  the  galvanometer.  Note  the  direction  of  the 
deflection.  Observe  the  effect  of  removing  the  magnet.  Repeat 
till  you  are  sure  of  the  results.  (The  galvanometer  must  be  far 
enough  away  not  to  be  directly  affected  by  the  motion  of  the  mag- 
net. Test  this  by  inserting  and  withdrawing  the  magnet  with  the 
circuit  broken.)  From  the  direction  of  the  deflection,  determine 
the  direction  of  the  current  round  the  coil  (clockwise  or  counter 
clockwise  as  you  look  down  upon  it),  when  the  north  pole  of  the 
magnet  is  inserted  and  when  it  is  removed.  Applying  the  right- 
hand  rule,  determine  whether  the  current  induced  in  the  coil 
makes  its  upper  end  N  or  S  when  the  north 
pole  of  the  magnet  is  inserted  and  when  it  is 
removed. 

Draw  diagrams  similar  to  Figure  in,  show- 
ing the  polarity  of  the  magnet  and  the  direc- 
tion in  which  it  is  moving,  and  the  resulting 
polarity  of  the  coil  and  direction  of  the  current 
round  it. 

c.  Is  there  a  current  when  the  magnet  is  at 
rest  within  the  coil?    What  is  the  experimental 
evidence  ? 

d.  Study  the  effect  of  inserting  and  removing  the  south  pole  of 
the  magnet.     Answer  all  the  questions  of  (^)  for  this  case,  and  draw 
diagrams  as  before. 


240 


ELECTRICITY 


Experiment  137.  —  To  study  the  laws  of  current  induction  by 
currents. 

Experimental  Work.  —  a.  Connect  the  cell  with  the  smaller 
coil  (called  the  primary)  so  as  to  make  the  lower  end  of  the  coil  a 
north  pole.  The  galvanometer  is  to  be  connected  with  the  sec- 
ondary coil  as  before. 

Determine,  from  the  deflection  of  the  needle,  the  direction  of 
the  current  in  the  secondary  coil  when  the  north  pole  of  the  pri- 
mary coil  is  inserted  into  and  when  it  is  removed  from  the  sec- 
ondary coil.  Make  diagrams  similar  to  Figure  112,  showing  the 
direction  of  the  current  in  the  secondary  coil  in 
each  case  and  the  resulting  polarity  of  this  coil. 
b.  With  the  primary  coil  at  rest  in  the 
secondary,  study  the  currents  induced  when 
the  circuit  is  closed  through  the  primary,  and 
when  it  is  broken.  (Make  and  break  the  cir- 
cuit by  touching  the  connecting  wire  to  one  of 
the  binding  posts,  and  removing  it.) 

Compare  the  directions  of  the  induced  cur- 
rents with  the  directions  of  the  currents  induced 
when  the  primary  coil  was  inserted  and  removed. 
Repeat  the  work  of  (b)  with  the  iron  core  within  the  primary 
Note  whether  the  deflections  are  greater  or  less  than  be- 
State  and  account  for  the  effect  of  the  core. 
d.  With  the  primary  circuit  closed,  insert  and  remove  the  pri- 
mary coil  and  the  iron  core  together,  first  quickly,  then  more  and 
more  slowly,  and  note  the  effect  of  the  rate  of  motion  on  the 
amount  of  the  deflection.  What  law  of  electro-magnetic  induc- 
tion is  illustrated? 


FIG.  112. 


c. 

coil, 
fore. 


Discussion.  — The  induced  current  in  the  secondary  coil  is 
called  direct  if  its  direction  round  the  coil  is  such  that  like  poles 
of  the  secondary  coil  and  the  magnet  or  the  primary  coil  point  in 
the  same  direction;  inverse,  if  their -like  poles  point  in  opposite 


THE   ELECTRIC   MOTOR   AND   DYNAMO  241 

directions.  Thus  a  direct  induced  current  flows  in  the  same 
direction  round  the  coil  as  the  inducing  current  in  the  primary 
coil,  and  an  inverse  induced  current  flows  in  the  opposite  direc- 
tion. State  the  different  ways  in  which  you  obtained  — 

1.  An  inverse  induced  current. 

2.  A  direct  induced  current. 

3.  Does  the  magnetic  field  due  to  the  induced  current  aid  or 
oppose  the  insertion  and  removal  of  the  magnet  or  the  primary 
coil?     (Consult  the  text  and  reference  books  for  a  discussion  of 
the  connection  of  this  fact  with  the  principle  of  the  conservation 
of  energy.) 

4.  In  which  cases  in  these  experiments  was  the  induced  cur- 
rent due  to  an  increase  in  the   strength  of  the  magnetic  field 
within  the  secondary  coil?     Was  the  induced  current  in  these 
cases  direct  or  inverse? 

5.  In  which  cases  was  the  induced  current  due  to  a  decrease  in 
the  strength  of  the  magnetic  field  within  the  secondary  coil  ?    Was 
the  induced  current  in  these  cases  direct  or  inverse? 

6.  What  law  of  electro-magnetic  induction  is  illustrated  by  the 
effect  of  the  iron  core  ? 

EXERCISE    73.     THE   ELECTRIC   MOTOR   AND 
DYNAMO 

References.  —  Adams,  513-523  ;  Coleman,  500-505  ;  Car.  &  C., 
493-500;  Ches.  G.  &  T.,  428-436,  439-441;  Hoad.  Br.,  406- 
415,  439;  Hoad.  El.,  445-459;  Mumper,  292-295;  Jackson, 
195-215  ;  Mil.  &  G.,  416-427  ;  Went.  &  H.,  314-325. 

Experiment  138. —  To  study  the  construction  and  action  of  a 
small  motor. 

Apparatus.  —  Small    motor    (Fig.    113);    dry   cell;    compass; 
small  square  of  cardboard;    iron  filings  in    sifter;    screw-driver; 
connecting  wires.     [The  cheapest  grade  of  motor  is  not  recom- 
mended.    One  costing  $2.00  to  $3.00  gives  much  better  service.] 
COLEMAN'S  NEW  MANUAL — 16. 


242 


ELECTRICITY 


FIG.  113. 


Experimental  Work.  —  a.   Trace  the  circuit  from  one  binding 
post  of  the  motor  to  and  from  the  armature,  and  through  the 

coil  of  the  field  magnet  to 
the  other  post.  (The  cir- 
cuit through  the  armature 
will  be  studied  later.)  If 
the  armature  and  the  coil 
of  the  field  magnet  are  con- 
nected in  series,  the  motor 
is  said  to  be  series-wound ; 
if  they  are  connected  in 
parallel,  it  is  shunt-wound. 
Is  this  motor  shunt  or  series 
wound? 

b.  Connect  the  motor 
with  the  dry  cell,  and  note 
by  which  post  the  current  enters  it.  Determine  the  polarity  of  the 
field  magnet  from  the  known  direction  in  which  the  current  flows 
round  its  coil  (applying  the  right-hand  rule),  and  test  your  con- 
clusion by  means  of  the  compass. 

Note  the  brush   (upper  or  lower)   by  which  the  current  enters 
the  armature,  and  the  direction  in  which  the  armature  rotates. 

c.  Interchange  the  battery  connections  with  the  binding  posts 
of  the   motor.     Does  this   reverse   the   direction  of  the   current 
in  the  coil  of  the  field   magnet?     Is   the   polarity  of  the   field 
magnet   reversed?      (Test   with    the   compass.)      Does    the  cur- 
rent enter  the  armature   by  the    same    brush   as  before    or   by 
the  other  one?     Does  the  armature  rotate  in  the  same  direction 
as  before? 

d.  Unscrew  the  horizontal  bar  that  supports  the  armature  on 
the  side  opposite  the  commutator  brushes.     (The  upper  side 'of 
this  bar  should  be  distinguished  by  a  file  mark,  to  assist  in  re- 
placing it  with  the  same  side  up.     There    are   commonly  slight 
inequalities  in  the  bar  which  throw  the  armature  slightly  out  of 
position   and   hinder   or   even  prevent  its  rotation,  if  the  bar  is 


THE   ELECTRIC   MOTOR   AND   DYNAMO  243 

reversed  when  it  is  replaced.)  Remove  the  armature  and  inspect 
the  winding  of  its  coils  and  their  connection  with  the  segments  of 
the  commutator.  Pass  a  current  through  the  armature  by  hold- 
ing the  ends  of  the  connecting  wires  from  the  cell  against  any  two 
segments  of  the  commutator;  and,  while  doing  so,  test  the 
polarity  of  each  pole  of  the  armature  by  means  of  the  compass. 
Draw  a  diagram  of  the  armature,  indicating  the  segment  of  the 
commutator  by  which  the  current  enters  and  the  one  by  which  it 
leaves  the  armature,  the  direction  of  the  current  in  each  coil,  and 
the  polarity  of  the  different  poles. 

e.  Test  the  polarity  of  the  poles  of  the  armature  when  the  con- 
necting wires  are  pressed  with  thumb  and  finger  against  opposite 
sides  of  the  commutator  and  the  armature  is  turned  into  different 
positions,  bringing  different  pairs  of  the  commutator  segments 
into  contact  with  the  connecting  wires.  Continue  this  study 
until  you  have  determined  at  what  two  points  in  a  complete  rota- 
tion the  current  is  reversed  in  any  one  coil  (the  wires  being  held 
opposite  to  each  other  in  fixed  positions,  like  the  brushes  of  the 
motor). 

/.  Send  the  current  from  the  cell  through  the  coil  of  the  field 
magnet,  turn  the  magnet  into  a  horizontal  position  with  the 
brushes  underneath,  place  the  cardboard  over  the  magnet,  and 
study  the  magnetic  field  in  the  space  where  the  armature  belongs, 
by  means  of  iron  filings  sprinkled  on  the  cardboard.  (If  the 
motor  is  series-wound,  the  circuit  through  the  field  magnet  will 
be  broken  by  the  removal  of  the  armature.  It  can  be  closed  by 
bringing  the  brushes  into  contact  with  each  other.)  Make  a 
diagram  of  the  poles  of  the  magnet  and  the  lines  of  force  between 
them.  Test  the  strength  of  the  magnet  after  breaking  the  cir- 
cuit, by  observing  its  effect  on  the  iron  filings  and  the  compass. 
This  residual  magnetism,  as  it  is  called,  is  important  in  most 
forms  of  dynamos,  but  is  of  no  value  in  motors. 

g.  Replace  the  armature  in  position,  and  test  it  by  finding 
whether  it  will  run  as  before.  Trace  the  direction  of  the  current 
(with  the  circuit  open)  from  either  post  to  the  other,  round  the 


244 


ELECTRICITY 


coil  of  the  field  magnet  and  all  the  coils  of  the  armature ;  and 
determine  by  the  right-hand  rule  the  resulting  polarity  of  the 
field  magnet  and  the  polarity  of  any  coil  of  the  armature  in  the 
different  parts  of  a  complete  rotation.  If  this  is  correctly  done, 
it  will  be  seen  that  the  commutator  reverses  the  current  in  each 
coil  of  the  armature  as  it  passes  two  fixed  positions  in  each 

rotation,  and  that  this  keeps  the 
armature  in  continuous  rotation  by 
the  attraction  of  unlike  poles  and  the 
repulsion  of  like  poles  of  armature 
and  field  magnet. 

Make  a  section  diagram  of  the 
motor,  similar  to  Figure  114,  and  in 
it  indicate  the  direction  of  the  cur- 
rent in  the  coils  of  the  field  magnet 
and  the  armature,  the  polarity  of  the 
field  magnet  and  the  poles  of  the 
armature,  and  the  direction  of  rota- 
tion. 


FIG.  114. 


h.  Account  for  the  direction  of  rotation  (the  same  or  opposite) 
when  the  direction  of  the  current  through  the  motor  is  reversed. 

Experiment  139. —  To  study  the  action  of  the  motor  when  run 
as  a  dynamo. 

Apparatus.  —  The  same  as  for  the  preceding  experiment,  to- 
gether with  a  low-resistance  galvanometer  or  galvanoscope  and  a 
piece  of  stout  cord  four  or  five  feet  long. 

Experimental  Work.  —  a.  Connect  the  motor  with  the  gal- 
vanometer, using  all  the  turns  of  the  coil.  Pass  an  end  of  the 
cord  half  round  the  pulley  attached  to  the  axle  of  the  armature ; 
and,  while  another  pupil  holds  the  motor  on  the  table,  set  the 
armature  in  rapid  rotation  by  drawing  the  cord  quickly  from  end 
to  end  over  the  pulley.  This  should  generate  sufficient  current  to 
deflect  the  galvanometer. 


THE   ELECTRIC   MOTOR  AND   DYNAMO  245 


Note  the  direction  of  the  deflection  when  the  armature  is 
rotated  in  the  same  direction  as  that  in  which  it  turns  as  a  motor, 
and  also  when  rotated  in  the  opposite  direction.  From  the  direc- 
tion of  the  deflection  in  each  case,  determine  the  direction  of  the 
current  through  the  galvanometer  (making  a  test  of  the  galvanom- 
eter by  means  of  the  cell,  if  necessary),  and  from  this  the  direction 
of  the  current  through  the  armature. 

b.  The  current  generated  by  the  rotation  of  the  armature  in 
this   experiment  is  too  weak  either  to   materially  strengthen  or 
weaken  the  residual  magnetism  of  the  field  magnet.     The  polar- 
ity of  this  residual  magnetism  is  determined  by  the  direction  of 
the  much   stronger   current  last  sent  through  the  coil  from  the 
cell.     Find  this  polarity  by  means  of  the  compass,  and  indicate 
it  in  a  diagram  like  that  of  the  motor  in  the  preceding  experi- 
ment. 

In  running  the  machine  effectively  as  a  dynamo,  the  direction 
of  the  current  generated  must  be  such  as  to  strengthen  the  exist- 
ing polarity  of  the  field  magnet.  In  which  direction  (the  same 
as  that  in  which  it  turns  as  a  motor  or  the  opposite)  must  the 
armature  be  turned  to  accomplish  this  result  ?  When  the  rotation 
is  in  this  direction,  does  the  current  flow  through  the  armature  in 
the  same  direction  as  when  it  is  running  as  a  motor,  or  in  the 
opposite  direction?  (The  answers  to  these  questions  are  not  the 
same  for  shunt-wound  as  for  series-wound  machines.  Remember 
that  the  current  enters  the  armature  by  the  positive  brush  when 
the  machine  is  run  as  a  motor,  and  leaves  by  the  positive  brush 
when  it  is  run  as  a  dynamo.) 

c.  Represent  the  above  facts  in  the  diagram  of  the  dynamo. 
State  the   points    of  resemblance  and    the  points  of  difference 
between  the  diagrams  of  the  motor  and  the  dynamo. 

Discussion  (Oral). —  i.  Does  the  current  generated  in  a  dynamo 
help  or  hinder  the  rotation  of  its  armature?  Answer  from  the 
facts  of  the  experiment,  as  shown  in  your  diagrams. 

2.  Show  that  the  laws  of  electro-magnetic  induction  apply  in 
the  generation  of  a  current  by  a  dynamo. 


246 


ELECTRICITY 


EXERCISE  74.     THE  GILLEY  GRAMME  RING  DYNAMO 
AND   MOTOR 

References.  —  The  same  as  for  Exercise  72. 

Experiment  140. —  To  study  the  construction  and  action  of  a 
model  Gramme  ring  dynamo  and  motor. 

Apparatus.  —  Gilley's  model  Gramme  ring  and  motor  (Fig.  115)  ; 
two  dry  cells ;  cardboard ;  iron  filings  in  sifter ;  compass ;  con- 
necting wires. 

[The  Gilley  model  Gramme  ring  and  motor  is  manufactured  by 
the  L.  E.  Knott  Apparatus  Co.,  Boston.  It  is  a  very  instructive 

piece  of  apparatus,  espe- 
cially designed  for  labora- 
tory work.  The  following 
directions  are  adapted 
from  Mr.  Gilley's  exer- 
cises on  the  machine.] 


FIG.  115. 


Experimental   Work. — 

The  Field  Magnet.  a. 
Lift  the  armature  off  and 
set  it  aside.  Send  the  cur- 
rent from  one  cell  through 
the  coil  of  the  field  mag- 
net. Lay  the  cardboard 
over  it,  and  study  the 
magnetic  field  by  means  of  iron  filings  and  the  compass.  Make  a 
diagram  of  the  field  magnet,  showing  the  direction  of  the  current 
round  the  coil,  the  north  and  south  poles  of  the  magnet,  and  the 
lines  of  force  between  the  poles. 

b.  Note  the  behavior  of  the  compass  needle  and  the  iron  filings 
when  the  circuit  is  closed,  and  when  it  is  open.  The  stronger  the 
magnetic  force,  the  more  rapidly  will  the  compass  needle  vibrate 


THE   GILLEY  GRAMME   RING   DYNAMO   AND    MOTOR     247 

when  disturbed.  The  magnetism  remaining  in  the  electro-magnet 
when  there  is  no  current  through  its  coil  is  called  residual 
magnetism.  What  do  you  infer  concerning  the  relative  amount 
of  the  residual  magnetism? 

c.  Reverse 'the  current  through  the  coil,  and  note  the  effect  on 
the  polarity  of  the  field  magnet.  Result? 

The  Armature.  —  d.  Remove  the  field  magnet  and  replace  the 
armature.  Send  the  current  from  one  cell  through  the  armature 
by  connecting  the  cell  with  the  binding  posts  on  the  brush  holder. 
Observe  that  there  is  a  continuous  coil,  wound  throughout  in  the 
same  direction  round  the  iron  ring  of  the  armature,  and  that  this 
coil  is  connected  at  four  equidistant  points  with  the  correspond- 
ing sections  of  the  commutator  on  the  under  side.  The  current 
divides  in  passing  through  the  armature  from  one  brush  to  the 
other,  part  going  through  one  half  of  the  coil  and  part  through 
the  other  half.  The  current  flows  in  opposite  directions  round 
these  two  parts  of  the  coil.  (Why?)  A  Gramme  ring  armature 
is,  therefore,  a  double  electro- magnet,  with  like  poles  of  the  two 
semicircular  magnets  together. 

Place  the  cardboard  over  the  armature,  and  study  its  magnetic 
field  by  means  of  the  iron  filings  and  the  compass.  The  double 
north  and  south  poles  of  the  armature  are  where  the  lines  of 
force  extend  radially  (i.e.  where  the  compass  points  exactly  toward 
the  center  of  the  armature).  Make  a  diagram  of  the  armature, 
representing  its  north  and  south  poles,  the  lines  of  force,  and  the 
direction  of  the  current  round  the  halves  of  the  coil. 

The  Commutator.  —  e.  With  the  current  flowing  through  the 
armature  and  the  cardboard  removed,  hold  the  compass  close 
beside  the  armature  at  one  of  its  poles ;  and,  keeping  it  in  this 
position,  note  the  behavior  of  the  needle  as  you  slovyly  turn  the 
armature.  Stop  the  armature  at  the  instant  when  the  needle  sud- 
denly changes  its  direction,  and  observe  whether  this  is  a  position 
in  which  the  brushes  change  contact  from  one  section  of  the 
commutator  to  the  next. 

Again  turn  the  armature  slowly,  moving  the  compass  at  the 


248  ELECTRICITY 

same  time,  so  as  to  keep  it  exactly  at  one  of  the  poles.  Stop  the 
armature  at  the  instant  when  the  needle  indicates  a  sudden  change 
in  the  position  of  the  pole,  and  find  the  point  to  which  the  pole 
has  shifted.  Find  what  change  of  contact  between  the  commuta- 
tor and  brushes  caused  the  shifting  of  the  pole.  Does  the  other 
pole  shift  at  the  same  time  so  as  to  remain  opposite  to  the  first? 

/.  How  many  times  during  a  complete  rotation  do  the  poles 
shift  to  a  new  position?  Why? 

Through  what  angle  do  the  poles  turn  with  the  armature  before 
shifting  to  a  new  position?  Through  what  angle  do  they  shift? 
Do  they  shift  in  the  direction  of  rotation  or  in  the  opposite 
direction? 

What  is  the  greatest  angle  that  the  straight  line  through  the  poles 
of  the  armature  makes  in  either  direction  with  the  line  through 
the  points  of  contact  of  the  brushes  with  the  commutator? 

g.  How  would  these  results  differ  if  the  commutator  had  eight 
sections?  sixteen  sections?  (The  commutators  of  dynamos  and 
motors  for  practical  use  have  many  sections.) 

h.  Find  the  north  and  south  poles  of  the  armature ;  then, 
without  changing  its  position,  turn  the  brush  holder  through  180°. 
What  is  the  effect  on  the  position  of  the  north  and  south  poles? 
Explain. 

The  Complete  Motor,  Series-wound.  —  /.  Place  the  armature  and 
the  field  magnet  in  position.  Connect  the  two  cells  in  series,  and 
join  one  pole  of  the  battery  to  a  binding  post  of  the  field  magnet, 
and  the  other  pole  to  one  of  the  binding  posts  on  the  brush  holder. 
Connect  the  other  binding  posts  of  the  field  magnet  and  brush 
holder  by  a  short  wire.  The  motor  is  now  series -wound.  Turn 
the  brush  holder  till  the  points  of  contact  of  the  brushes  are  in  a 
line  parallel  to  the  two  arms  of  the  field  magnet.  The  armature 
should  rotate. 

Make  a  diagram  of  the  motor,  showing  the  connections,  the 
direction  of  the  current  round  the  coil  of  the  field  magnet  and 
the  two  branches  of  the  armature  coil,  the  polarity  of  the  field 
magnet  and  the  armature,  and  the  direction  of  rotation.  If  you 


THE  GILLEY. GRAMME   RING   DYNAMO  AND   MOTOR     249 

have  difficulty  in  determining  the  polarity  of  the  armature  either 
by  the  right-hand  rule  or  the  compass,  test  it  with  the  compass 
after  removing  the  coil  of  the  field  magnet  from  the  circuit. 

Referring  to  your  diagram,  show  whether  all  the  attractions: 
and  repulsions  between  the  poles  of  the  field  magnet  and  the 
poles  of  the  armature  are  such  as  to  cause  rotation  in  the  observed 
direction. 

j.  With  the  connections  the  same  as  before,  turn  the  brush 
holder  through  180°.  Account  for  the  reversal  of  the  rotation. 

k.  Turn  the  brush  holder  back  through  90°,  bringing  the  points 
of  contact  of  the  brushes  into  a  line  at  right  angles  to  the  arms  of 
the  field  magnet.  Why  does  the  armature  not  rotate  ? 

The  Complete  Motor,  Shunt-wound. — /.  Connect  the  battery 
wires  to  the  binding  posts  of  the  field-magnet  coil,  and  connect 
the  armature  as  a  shunt  to  this  coil.  The  motor  is  now  shunt- 
wound.  The  position  of  the  brush  holder  is  the  same  as  with 
series  winding.  Make  a  diagram  showing  connections,  direction 
of  rotation,  etc.,  as  before. 

m.  Is  the  rotation  reversed  on  turning  the  brush  holder  through 
180°?  Give  reason. 

n.  Is  the  rotation  reversed  on  interchanging  the  battery  con- 
nections ?  Explain. 

Experiment  141. —  To  study  the  action  of  the  model  Gramme 
ring  machine  when  run  as  a  dynamo. 

Apparatus.  — The  same  as  for  the  preceding  experiment,  to- 
gether with  a  low-resistance  galvanometer. 

Experimental  Work.  —  a.  Restore  the  connections  and  the 
adjustment  of  the  brush  holder  exactly  as  shown  in  your  diagram 
under  (/)  in  the  preceding  experiment.  See  that  the  direction  of 
rotation  is  the  same  as  before,  and  note  by  which  binding  post 
the  current  enters  the  armature.  (This  is  the  positive  armature 

post.) 

Disconnect  the  armature  from  the  battery  circuit,  leaving  the 


250  ELECTRICITY 

field  magnet  in  the  circuit  as  it  was ;  and  connect  the  armature 
with  the  galvanometer,  using  all  its  turns.  Rotate  the  armature 
as  rapidly  as  possible,  by  a  sudden  push  of  the  finger,  in  the  direc- 
tion in  which  it  previously  turned  as  a  motor,  and  note  the  direc- 
tion of  the  galvanometer  deflection.  From  the  direction,  of  the 
deflection,  find  the  direction  of  the  current  in  the  armature  circuit 
(testing  the  galvanometer  with  a  cell,  if  necessary),  and  note  the 
post  by  which  the  current  leaves  the  armature.  This  is  the  posi- 
tive post,  since  the  E.  M.  F.  is  generated  in  the  armature  coil  and 
the  rise  of  potential  must  therefore  be  in  it. 

Does  the  current  flow  in  the  same  direction  in  the  armature  as 
it  did  when  the  machine  was  running  as  a  motor,  or  in  the  oppo- 
site direction?  Draw  a  diagram  as  for  the  motor,  representing 
the  direction  of  the  current  in  the  coils  of  the  field  magnet  and 
armature,  the  polarity  of  the  field  magnet,  and  the  polarity  of  the 
armature  resulting  from  the  current  generated  by  its  rotation. 

b.  Find  in  the  same  way  the  direction  of  the  current  generated 
by  rotating  the  armature  in  the  opposite  direction,  all  the  other 
conditions  remaining  the  same  as  before. 

Leave  the  cells  disconnected. 

Discussion.  —  i.  Is  the  polarity  of  the  armature  such  as  to  aid 
or  oppose  its  rotation  when  it  is  run  as  a  dynamo?  Show  that  the 
answer  is  in  agreement  with  the  principle  of  the  conservation  of 
energy,  and  that  if  the  opposite  were  true,  it  would  be  an  excep- 
tion to  this  principle. 

2.  From  a  comparison  of  your  diagrams,  show  whether  (the 
connections  remaining  the  same)  the  armature  of  a  shunt-wound 
dynamo  must  be  turned  in  the  direction  in  which  it  would  run  as 
a  motor,  or  in  the  opposite  direction,  if  it  supplies  the  current  for 
its  own  field  magnet.    (The  direction  of  the  current  that  a  dynamo 
sends  through  its  field  magnet  must  be  such  as  to  strengthen  the 
existing  polarity  of  the  residual  magnetism.     Why?) 

3.  What  is  the  advantage  of  a  large  number  of  segments  in  the 
commutator  of  a  motor? 


THE  TELEPHONE 


EXERCISE    75.     THE   TELEPHONE 


251 


References. — Adams,  530-532  ;  Coleman,  508-510;  Car.  &  C., 
520-523  ;  Ches.  G.  &  T.,  446  ;  Hoad.  Br.,  429-431  ;  Hoad.  EL, 
469-471  •  Mumper,  299  ;  Jackson,  308-316  ;  Mil.  &  G.,  441-443  ; 
Went.  &  H.,  332. 

Experiment  142. —  To  study  the  construction  and  action  of  a 
telephone  receiver. 

Apparatus.  —  A  d'Arsonval  or  astatic  galvanometer  of  high 
resistance ;  telephone  receiver. 

Experimental  Work.  —  a.  Unscrew  and  remove  the  cap  that 
covers  the  disk  of  the  receiver.  Remove  the  disk.  Describe  the 
parts  exposed  to  view.  Is  the  disk  attracted  by  the  magnet?  Of 
what  material  is  it?  Make  a  section  diagram  of  the  receiver. 

b.  Connect  the  receiver  with  the  galvanometer.     Note  the  be- 
havior of  the  galvanometer  when  you  touch  the  magnet  with  the 
disk,  and  again  when  you  remove  the  disk.     Do  the  deflections 
indicate  currents  in  the  same  or  in  opposite  directions  in  the  two 
cases?     Account  for  these  currents. 

c.  Place   the   disk  in  position  on  the   receiver,  and   observe 
whether  the  galvanometer  indicates  a  current  when  you  press  the 
disk  lightly  at  its  center  with  the  finger,  so  as  to  bring  it  nearer 
the  magnet,  and  again  when  you  remove  the  pressure. 

If  you  should  speak  into  the  receiver  when  it  is  on  a  closed 
circuit,  what  currents  would  be  generated,  and  why?  Why  would 
such  currents  not  cause  a  deflection  of  the  galvanometer? 

Experiment  143. —  To  study  the  action  of  a  telephone  line  con- 
sisting of  two  receivers. 

Apparatus.  —  Two  telephone  receivers  at  opposite  ends  of  the 
laboratory  or  in  adjacent  rooms,  connected  with  long  wires ;  tun- 
ing fork ;  rubber  mallet. 

[The  circuit  may  be  permanently  set  up  between  two  binding 


252  ELECTRICITY 

posts  at  each  end  of  the  line,  so  that  it  is  only  necessary  for  the 
pupil  to  connect  the  receivers  with  the  binding  posts.] 

Experimental  Work.  —  a.  Listen  at  one  receiver  while  your 
companion  touches  the  stem  of  a  vibrating  fork  to  the  disk  of  the 
receiver  at  the  other  end  of  the  line. 

b.  Try  speaking  to  one  another,  using  the  receivers  alternately 
as  receiver  and  transmitter. 

Explain  the  action  of  such  a  telephone  line. 

Experiment  144.  —  To  study  the  construction  and  action  of  a 
microphone. 

Apparatus.  —  Telephone  receiver;  dry  cell;  two  battery  or 
electric  light  carbons ;  microphone  ;  tuning  fork  and  rubber  mal- 
let ;  watch. 

Experimental  Work.  —  a.  Connect  the  pieces  of  carbon,  the 
receiver,  and  the  battery  as  shown  in  Figure  116,  so  that  the  circuit 

will  be  closed  by  touching 
the  carbons  together.  Place 
the  receiver  to  the  ear,  and 
touch  one  carbon  to  the 
other,  varying  the  pressure, 
or  rub  one  carbon  lightly 
over  the  other.  The  re- 
ceiver should  give  out  a 

loud,   rattling   sound.     The 
FIG.  116.  .  '  5 

resistance  at  the  points  of 

contact  of  the  carbons  with  each  other  varies  with  the  pressure. 
How  does  this  account  for  the  sounds  from  the  receiver? 

b.  If  the  microphone  is  without  an  induction  coil,  connect  it 
in  series  with  the  receiver  in  the  battery  circuit  (Fig.  117)  ;  if 
it  has  an  induction  coil,  connect  the  cell  with  the  primary  coil 
and  the  telephone  receiver  with  the  secondary.  (The  microphone 
is  permanently  connected  in  series  with  the  primary  coil.) 

Hold  the  receiver  to  the  ear,  and  tap  lightly  on  the  base  of  the 


THE  TELEPHONE 


253 


microphone,  or  rub  the  finger  lightly  over  it.  Listen  to  a  watcn 
lying  on  the  microphone.  Touch  a  faintly  sounding  tuning  fork 
to  the  microphone. 


FIG.  117. 

How  does  the  microphone  reproduce  these  different  sounds? 
Is  the  reproduction  like  the  original  sound  in  character?  Is  it 
louder  ? 

Experiment  145.  —  To  study  the  construction  and  action  of  a 
complete  telephone  line. 

Apparatus.  — A  telephone  line  consisting  of  two  telephones 
made  for  laboratory  use. 

[A  battery  call  telephone  (Fig.  118),  costing  from  $5  to  $7 
each,  is  suitable  for  this  experiment.] 

Experimental  Work.  —  The  principles  of  the  modern  telephone 
are  covered  by  the  preceding  experiments ;  the  details  of  con- 
struction differ  in  different  telephones.  The  following  general 
directions  indicate  the  principal  matters  of  detail  to  be  made  out 
in  the  study  of  the  laboratory  telephone. 


254 


ELECTRICITY 


a.  Trace  out  the  connections  by  which  the  bell  is  included  in 
th.e  line  circuit  when  the  receiver  is  on  the  hook. 

b.  Trace  the  line  circuit  through  the  telephone  when  the  button 

is  pushed  to  ring  the  bell  of  the 
other  telephone.  Is  the  bell  of 
one  telephone  rung  by  the  bat- 
tery of  the  other,  or  by  its  own? 

c.  With  the  receiver  off  the 
hook,   trace    the    local    circuit 
through  the  transmitter  and  the 
primary  coil,  and  the  line  cir- 
cuit through  the  secondary  coil 
and  the  receiver. 

What  connections  are  broken 
and  what  made  by  the  lever 
when  the  receiver  is  removed 
from  the  hook? 

d.  Study  and  use  the  line  till 
you  understand   its    operation. 
Draw  one  or  more  diagrams  of 

the  telephone,  showing  the  various  circuits  and  connections  that 
you  have  found.  Describe  the  telephone  and  its  action,  referring 
to  your  diagrams. 


FIG.  118. 


EXERCISE    76.      ELECTROLYSIS    AND    THE    STORAGE 

CELL 

References.  —  Adams,  533-538  ;  Coleman,  511-513;  Car.  &C., 

445-44 7>  449-45 1  ',  Ches.  G.  &  T.,  395~395  a  \  Hoad-  Br->  365- 
370;  Hoad.  El.,  415-420;  Mumper,  269-271  ;  Jackson,  56-67, 
370-387  ;  Mil.  &  G.,  387-393  ;  Went.  &  H.,  306-307,  309-312. 

Experiment  146.  —  To  study  the  effect  of  passing  an  electric  cur- 
rent through  solutions  of  zinc  sulphate  and  copper  sulphate,  between 
copper  and  other  electrodes. 


ELECTROLYSIS   AND   THE   STORAGE  CELL  255 

Apparatus. — Two  dry  or  chromic  acid  cells;  tumbler  of  zinc 
sulphate  in  solution  (colorless)  ;  tumbler  of  copper  sulphate  in 
solution  (blue)  \  copper  wires,  No.  16  or  larger,  bare  or  bared  for 
about  10  cm.  at  the  ends  ;  piece  of  emery  cloth  or  sandpaper. 

Experimental  Work.  —  a.  Connect  the  cells  in  series,  and  use 
the  bare  copper  wires  (or  wires  bared  for  about  10  cm.  at  the  ends) 
as  the  battery  terminals.  Brighten  with  the  emery  cloth  the  free 
end  of  the  negative  terminal.  The  free  end  of  the  positive  termi- 
nal should  be  dull  from  exposure  to  the  air.  If  it  is  bright  or 
plated  with  zinc  from  previous  use,  cut  this  portion  off  or  use 
another  wire. 

Hold  the  battery  terminals  some  distance  apart  in  the  solution 
of  zinc  sulphate,  and  close  the  circuit.  Note  any  immediate 
change  in  the  appearance  of  either  terminal.  Remove  them  occa- 
sionally for  better  observation.  Which  terminal  (the  positive  or 
the  negative)  receives  a  coating  of  zinc?  What  evidence  do  you 
find  that  copper  from  the  other  terminal  has  gone  into  solution? 
The  electric  current  causes  copper  to  replace  zinc  in  the  com- 
pound, forming  copper  sulphate  and  depositing  zinc. 

b.  Place  a  brightened  end  of  copper  wire  in  the  zinc  sulphate 
solution  without  electrical  connection.     Is  it  coated  with  zinc? 
Do  you  infer  that  electrical  energy  is  or  is  not  necessary  for  this 
displacement  of  zinc  by  copper? 

c.  Place  the  zinc-covered  terminal  in  the  solution  of  copper 
sulphate  for  an  instant,  without  electrical  connections,  and  observe 
whether  the  coating  of  zinc  is  removed.     If  so,  is  there  any  evi- 
dence that  a  deposit  of  copper  has  taken  its  place  ?     Wipe  the 
wire  with  a  cloth  to  be  sure  of  results.     Is  a  supply  of  energy  from 
some  outside  source  necessary  for  this  displacement  of  copper 
from  the  sulphate  by  zinc? 

d.  Take  for  battery  terminals  wires  whose  free  ends  have  not 
been  used  or  brightened  ;  and,  with  the  circuit  closed*  hold  these 
ends  for  a  minute  or  two  in  the  solution  of  copper  sulphate.     De- 
termine from  the  appearance  of  the  wires  which  (the  positive  or 


256  ELECTRICITY 

the  negative)  has  received  a  deposit  of  copper  and  which  has  been 
partly  consumed.  Was  the  transfer  of  copper  between  the  termi- 
nals in  the  direction  of  the  current  or  in  the  opposite  direction? 

e.  If  you  wish  to  plate  a  nickel  or  a  dime  with  copper,  attach 
it  to  the  terminal  that  receives  the  deposit.  To  attach  the  coin, 
wrap  the  end  of  the  wire  four  or  five  times  round  a  lead  pencil, 
making  the  turns  close  together,  and  slip  the  coin  between  them. 
To  make  the  plating  uniform,  it  will  be  necessary  to  slip  the  wire 
into  a  new  position  on  the  coin  three  or  four  times. 

How  could  the  current  be  made  to  remove  the  plating? 

Experiment  147. —  To  study  the  construction  and  action  of  a 
storage  cell 

Apparatus.  —  Tumbler  containing  dilute  sulphuric  acid  (about 
10%  acid  by  volume)  ;  two  lead  plates,  with  support  as  in  Exer- 
cise 59;  two  dry  cells;  electric  bell;  high-resistance  galvanom- 
eter or  voltmeter ;  piece  of  emery  cloth  or  sandpaper ;  connecting 
wires ;  two  double  connectors. 

Experimental  Work.  —  a.  Clean  the  lead  plates  with  the  emery 
cloth  or  scrape  them  with  a  knife,  till  the  surfaces  are  bright. 
Place  them  in  the  tumbler  of  acid,  using  the  support  to  keep  them 
in  position,  and  connect  their  terminals  with  the  galvanometer  (or 
voltmeter).  If  all  deposits  due  to  previous  use  have  been  removed 
from  the  plates,  there  will  be  no  deflection.  The  tumbler  of  acid 
and  the  lead  plates  constitute  a  storage  cell.  In  its  present  con- 
dition its  E.  M.  F.  is  zero.  (Why?) 

b.  Connect  the  storage  cell  in  circuit  with  the  battery  of  dry 
cells,  and  connect  the  galvanometer  as  a  shunt  to  the  storage  cell 
(Fig.  119).  Note  the  deflection  (exact  reading  not  required). 
After  about  half  a  minute  disconnect  one  of  the  battery  terminals, 
and  note  the  behavior  of  the  galvanometer.  Does  it  indicate  an 
E.  M.  F.  in  the  storage  cell?  If  so,  note  the  rapidity  with  which 
the  deflection  decreases  as  the  cell  loses  its  slight  charge  in  send- 
ing a  current  through  the  galvanometer. 


ELECTROLYSIS   AND   THE   STORAGE   CELL  257 

c.  Again  close  the  battery  circuit  through  the  storage  cell  for 
about  half  a  minute,  and  repeat  the  previous  observations.     Note 
the  formation  of  bubbles  on  the  plates  during  the  charging.     Do 
they  gather  more    abundantly  on   the  positive    or   the   negative 
plate  ?    The  bubbles  at  the  positive  plate  are  of  oxygen  ;  those  at 
the  negative  plate,  of  hydrogen.     Raise 

the  lead  plates  out  of  the  liquid  and 
note  their  color,  especially  the  inside 
surface  of  each,  when  the  cell  is  charged 
and  also  when  it  is  discharged. 

d.  Repeat  all  these  processes  and  ob- 
servations five  or  six  times,  noting  care- 
fully  the   growing   color  of  the  plates 
when  charged,  the  difference  between 
the  color  of  the  plates  when  charged 
and  when  discharged,  and  the  increas- 
ing time  required  to  discharge  the  cell.     Repeated  charging  and 
discharging  increases  the  quantity  of  reddish  brown  peroxide  of 
lead  (PbO£)  that  can  be  formed  on  the  one  plate  (which?),  and 
the  quantity  of  spongy  lead  that  can  be    formed  on  the  other. 
The  cell  thus  becomes  capable  of  receiving  a  greater  charge. 

e.  Determine  from  the  direction  of  the  galvanometer  deflection 
whether  the  plate  that  is  positive  while  the  cell  is  being  charged 
is  also  the  positive  plate  while  the  cell  is  generating  a  current. 
Does  the  current  generated  by  the  cell  flow  through  it  in  the  same 
direction  as  the  charging  current  or  in  the  opposite  direction? 

f.  If  a  voltmeter  is  used,  find  the  voltage  of  the  cell  when 
charged. 

g.  Charge  the  cell,  and  connect  it  with  the  electric  bell.     It 
should    furnish    current   enough    to   ring    the    bell    for   several 
seconds. 

Discussion.  —  i.    Compare  the  chemical  changes  that  take  place 
in  the  zinc  sulphate  cell,  under  the  action  of  the  electric  current, 
with  those  that  take  place  in  the  gravity  or  the  Daniell  cell  in  gen- 
^OLEMAN'S  NEW  MANUAL —  17 


258  ELECTRICITY 

crating  a  current.     What  transformation  of  energy  do  you  infer 
takes  place  in  the  electrolytic  cell?     Give  reasons. 

2.  What  transformation  of  energy  takes  place  in  a  storage  cell 
while  it  is  being  charged?  while  it  is  generating  a  current? 

3.  To  what  extent  do  the  facts  established  in  this  exercise  lend 
support  to  the  principle  of  the  conservation  of  energy  ? 


APPENDIX 


TABLE   I 
DENSITIES  IN  GRAMS  PER  CUBIC  CENTIMETER 


Aluminum  . 

2.67 

Alcohol  (95  %)  . 

.82 

Antimony,  cast    . 

6.7 

Blood 

i.  06 

Beeswax 

.96 

Carbon  disulphide      , 

1.29 

Bismuth,  cast 

9.8 

Chloroform 

i-5 

Brass  . 

8.4 

Copper  sulphate  solution 

1.16 

Copper 

8.8  to     8.9 

Ether 

.72 

Cork    . 

.14  to     .24 

Glycerine  . 

1.27 

Galena 

7.58 

Hydrochloric  acid 

1.22 

German  silver 

8-5 

Mercury,  at  o°  C.       .     i 

3-596 

Glass,  crown 

2.5 

Milk 

1.03 

Glass,  flint  . 

3       to  3.5 

Nitric  acid 

15 

Gold    . 

19-3 

Oil  of  turpentine 

.87 

Ice       ... 

.917 

Olive  oil    . 

.915 

Iron,  bar 

7.8 

Sulphuric  acid  (15  %) 

1.  10 

Iron,  cast     . 

7.2  to    7.3 

Sulphuric  acid  . 

1.8 

Ivory  . 

1.9 

Water  (4°  C.)  . 

I.OOO 

Lead    . 

11.3   to  11.4 

Water,  sea 

1.026 

Marble 

2.72 

Mercury,  at  o°  C. 

I3-596 

GASES  AT  o°  C.  AND 

76  CM. 

Platinum 

21.5 

PRESSURE 

Quartz 

2.65 

Q'l 

,     _     - 

Air 

OOI293 

Steel    . 

7.8   to    7.9 

Carbon  dioxide 

.001977 

Sulphur,  native    . 

2.03 

Hydrogen 

.0000896 

Tin      . 

7-3 

Nitrogen    . 

.001256 

Zinc,  cast     . 

6.86 

Oxygen 

.001430 

25 

9 

260 


APPENDIX 


TABLE    II 
DENSITY  OF  WATER  AT  VARIOUS  TEMPERATURES 


TEMPERATURE 

DENSITY 

TEMPERATURE 

DENSITY 

0°        . 

.99987 

1  6°     . 

.99900 

4°      •         • 

I  .OOOOO 

20°      . 

.99826 

8°      . 

.99989 

50^      .            . 

.9882 

12°         . 

•99955 

100°       . 

.9586 

TABLE    III 

RELATIVE  CONDUCTIVITIES  FOR  HEAT 
(Silver  taken  as  the  standard  of  comparison  =  100.) 


Silver 

Copper 

Brass 

Zinc 

Tin 

Iron 

Lead 


Aluminum 
Brass    . 
Copper . 
Glass    . 
Gold 


100 

74 
27 

20 


8.5 


Bismuth 
Ice 

Marble    . 
Water     . 
Glass 
Wood     . 
Air 


TABLE   IV 
COEFFICIENTS  OF  LINEAR  EXPANSION 


.000023 

.0000188 

.0000172 

.0000085 

.0000144 


Iron  and  steel 
Lead     . 
Platinum 
Silver    . 
Hard  wood    . 


TABLE   V 
COEFFICIENT  OF  CUBICAL  EXPANSION 


Acetic  acid 

Alcohol  (5°  to  6°)     . 

Alcohol  (49°  to  50°) 

Ether 

Glycerine . 

Mercury   . 


.00105 

.00105 

.00122 

.0015 

.0005 

.00018 


Olive  oil 

Petroleum 

Turpentine 

Water  (5°  to  6°)      . 

Water  (49°  to  50°)  . 

Water  (99°  to  100°) 


2 

O.2 

0.15 

0.14 

0.05 

O.OI 

0.007 


.000012 

.000028 

.0000088 

.000019 

.000006 


.0008 
.0009 
.0007 

.000022 

.00046 

.00076 


APPENDIX 


26l 


TABLE   VI 

MELTING  POINTS 

Aluminum       . 

.      657°  C. 

Lead 

327°  c. 

Beeswax 

62 

Mercury     . 

-39 

Butter     . 

33 

Paraffine    . 

45  to  50 

Copper   . 

.     1084 

Platinum    . 

1775 

Glass 

.     1000  to  1400 

Rose's  fusible  metal  . 

94 

Gold       . 

.     1064 

Solder,  soft 

225 

Ice 

o 

Sulphur 

115 

Iridium   . 

.    1950 

Tin    . 

230 

Iron,  cast 

.       IIOO  tO   I2OO 

Wax,  white 

65 

TABLE  VII 

BOILING  POINT 

Acetic  acid 

.     ii7°C. 

Water 

100°  C. 

Alcohol,  ethyl 

.      78.4 

Air      . 

-  191 

Alcohol,  methyl 

.      66 

Ammonia    . 

-39 

Ether      . 

-       34  9 

Carbon  dioxide  . 

-78 

Mercury 

-     357 

Hydrogen   . 

-2385 

Sulphur  . 

.     447 

Nitrogen     . 

-  194-5 

Sulphuric  acid 

•     325 

Oxygen 

-  182 

TABLE   VIII 

SPECIFIC  HEATS 

Alcohol  (o°  to  50° 

)      .        .    .615 

.114. 

Aluminum  (15°  to 

97°)         •    -2i 

Lead 

.0^1 

Brass  . 

.    .094 

Marble 

.       .21 

Copper 

.    .095 

Mercury 

•       -033 

Ether  . 

.    .52 

Silver  .... 

.       .056 

Glycerine 

.     .55 

Steel 

.118 

Glass   . 

.     .19 

Turpentine  . 

.       .426 

Trp 

.COA 

Zinc    , 

.094 

262 


APPENDIX 


TABLE    IX 
HEATS  OF  FUSION 


CALORIES 

CALORIES 

Ice     . 

7Q  2C 

Silver          •         •         • 

2  1  .07 

Iron   •         •         • 

23  to  3O 

Sulphur      ... 

Lead  . 

•**j  cw  ow 

•      5-37 

Tin    . 

.      14.25 

.      2.83 

7i  n  r    . 

28  13 

TABLE   X 

HEATS  OF  VAPORIZATION 

CALORIES 

CALORIES 

Alcohol  . 

.    208 

Sulphur 

.    362 

Ether     . 

.      90 

Turpentine 

-     74 

Mercury          .         . 

62 

Watpr 

r?6 

TABLE   XI 

VELOCITY 

OF  SOUND  IN  METERS  PER  SECOND 

Brass 

3394 

GASES  AT  o  ° 

Glass 

4965  to  5564 

Air       .... 

•     332 

Granite  . 

1664 

Carbon  dioxide     . 

.     261 

Iron 

5016  to  5127 

Hydrogen     . 

.  1269 

Lead 

1319  to  1368 

Oxygen 

•     317 

Oak        ... 

3287  to  3991 

Steel       . 

4768  to  5016 

TABLE  XII 

INDICES  OF  REFRACTION 

Air   . 

i  .000294 

Ice     

1-31 

Alcohol     . 

1.36 

Iceland  spar,  ordinary  ray  . 

1.65 

Canada  balsam 

1.54 

Iceland  spar,  extraordinary 

Carbon  bisulphide 

1.68 

ray      . 

1.48 

Diamond  . 

2.47  to  2.75 

Water        . 

I-336 

Ether 

1.36 

The  eye  : 

Glass,  crown 

1.53  to  1.56 

Aqueous  humor 

1-337 

Glass,  flint 

1.58  to  1.64 

Vitreous  humor 

1-339 

Glycerine 

1.47 

Crystalline  lens 

1.384 

APPENDIX  263 

TABLE   XIII 
ELECTRIC  RESISTANCE 

(Ohms  to  i  m.  length  and  i  sq.  mm.  cross  section.) 


Aluminum,  annealed  .  .0289 

Copper,  annealed    .  .  .0157 

Copper,  hard .         .  .  .0150 

German  silver         .  .  .2076 

Iron,  pure        .         .  .  .0964 

Iron,  telegraph  wire  .  .15 


Lead          .         .  .  .196 

Manganin.         .  .  .475 

Mercury    .         .  .  .943 

Platinum  .         .  .  .0898 

Silver,  annealed  .  .0149 

Carbon,  graphite  .  24  to  420 


TABLE   XIV 
ELECTROMOTIVE  FORCE  OF  CELLS 

These   are   only  approximate   values.     The   E.M.F.  of  cells  varies 
considerably  with  the  condition  of  the  plates  and  the  liquid. 


VOLTS 


Bunsen     .         .  .  .  1.9 

Daniell     .         .  .  .  1.07 

Edison-Lalande  .  .  .7 

Gravity  I 


VOLTS 

Grenet       ....        2 
Grove        .         .         .         .         1.9 
Leclanche' .        .        .        .        i  .4 


TABLE  XV 
TANGENTS  OF  ANGLES 

To  find  the  tangent  of  an  angle  not  measured  by  a  whole  number 
of  degrees,  find  first  the  tangent  of  the  integral  part  of  the  number, 
and  add  to  this  the  product  obtained  by  multiplying  the  difference 
between  this  tangent  and  the  tangent  of  the  next  whole  number  of 
degrees  by  the  decimal  part  of  the  angle.  For  example,  to  find  the 
tangent  of  38°  .7,  proceed  thus :  — 

tan  38°  =  .781,  tan  39°  =  .810. 

.810  -  .781  =  .029, 

.7  x  .029  =  .020. 

tan  38°  .7  =  .781  +  .020  =  .801. 


264 


APPENDIX 


ANGLE 

TANGENT 

ANGLE 

TANGENT 

ANGLE 

TANGENT 

ANGLE 

TANGENT 

0° 

.OOOO 

23° 

.424 

46° 

.036 

69° 

2.6l 

I 

.0175 

24 

•445 

47 

.072 

70 

2.75 

2 

.0349 

25 

.466 

48 

.III 

71 

2.90 

3 

.0524 

26 

.488 

49 

.150 

72 

3.08 

4 

.0699 

27 

.510 

50 

.192 

73 

3-27 

5 

.0875 

28 

•532 

5i 

•235 

74 

3-49 

6 

.1051 

29 

•554 

52 

.280 

75 

3-73 

7 

.1228 

3° 

•577 

53 

•327 

76 

4.01 

8 

.1405 

3i 

.601 

54 

•376 

77 

4-33 

9 

.1584 

32 

.625 

55 

.428 

78 

4.70 

10 

.1763 

33 

.649 

56 

•483 

79 

5.14 

ii 

.194 

34 

.675 

57 

•540 

80 

5.67 

12 

.213 

35 

.700 

58 

.600 

81 

6-31 

13 

.231 

36 

•727 

59 

.664 

82 

7.12 

H 

.249 

37 

•754 

60 

•732 

83 

8.14 

15 

.268 

38 

.781 

61 

.804 

84 

9.51 

16 

.287 

39 

.810 

62 

.88 

85 

u-43 

17 

.306 

40 

•839 

63 

.96 

86 

14.30 

18 

•325 

4i 

.869 

64 

2.05 

87 

19.08 

19 

•344 

42 

.900 

65 

2.14 

oo 
oo 

28.64 

20 

•364 

43 

•933 

66 

2.25 

89 

57.29 

21 

•384 

44 

.966 

67 

2-36 

90 

00 

22 

.404 

45 

1.  000 

68 

2.48 

TABLE   XVI 

EQUIVALENTS 

cm. 

=  0-3937  in. 

in. 

—      2.54  cm. 

km. 

=  0.6214  mi- 

m. 

=       1.  609  km. 

sq.  cm. 

=  0.1550  sq.  in. 

sq.  in. 

=      6.452  sq.  cm. 

c.  cm. 

=  0.0610  cu.  in. 

cu.  in. 

=     16.387  ccm. 

kg- 

=  2.  20  Ib.  avoir. 

oz.  avoir. 

=    28.35  g. 

1. 

-  1.0567  qt.  (liquid). 

Ib.  avoir. 

=  453-6  g- 

1. 

=  0.908  qt.  (dry). 

ADAMS'S  PHYSICS 

By  CHARLES  F.    ADAMS,  A.  M.,  Head  of  the  Depart- 
ment of  Physics,  Central  High  School,  Detroit. 


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that  the  life  processes  of  plants  and  of  animals  are  similar,  and 
in  many  respects  identical ;  that  the  properties  and  activities 
of  protoplasm  are  the  same  whether  in  the  cell  of  a  plant  or 
of  an  animal ;  and  that  the  human  body  is  a  delicate  machine, 
built  out  of  that  same  mysterious  living  matter,  protoplasm. 
With  such  a  foundation  this  correlation  is  simple  and  natural. 
^f  The  course  is  designed  to  give  to  students  a  general  con- 
ception of  the  wide  range  of  forms  in  plant  and  animal  life  ; 
to  lead  them  to  observe  the  various  processes  carried  on  by 
plants  and  animals,  and  to  study  only  so  much  of  structure 
as  is  necessary  for  a  clear  comprehension  of  these  processes ; 
and  to  help  them  to  understand  the  general  structure  of  the  hu- 
man body,  and  the  way  to  care  for  it. 

^f  The  treatment  follows  the  order  in  which  the  topics  are 
likely  to  be  taken  up  when  the  work  is  begun  in  the  fall. 
The  laboratory  and  field  work  is  interesting  and  readily 
comprehended.  The  questions  are  few  and  simple;  they 
apply  to  structures  easily  found,  and  deal  with  externals  only. 
The  experiments  outlined  in  the  book  do  not  require  an  ex- 
tensive laboratory  equipment.  Excellent  results  may  be  ob- 
tained with  little  or  no  apparatus,  except  that  made  by  the 
pupils  and  teacher  working  together. 

*][  The  course  combines  in  excellent  proportion  text-book 
study,  laboratory  experiments,  field  work,  and  work  for 
oral  recitation,  and  is  attractive,  accurate,  and  informative. 


AMERICAN    BOOK    COMPANY 

(.68) 


A    NEW  ASTRONOMY 

$1-3° 

By  DAVID  TODD,  M.A.,  Ph.D.,  Professor  of  Astron- 
omy and  Navigation,  and  Director  of  the  Observatory, 
Amherst  College. 

ASTRONOMY   is .  here    presented    as   preeminently   a 
science   of  observation.      More    of  thinking    than   of 
memorizing^  required  in  its  study,  and  greater  emphasis 
is  laid  on  the  physical  than  on  the  mathematical  aspects  of 
the  science.      As  in  physics  and  chemistry  the  fundamental 
principles  are  connected  with  tangible,  familiar  objects,  and 
the  student  is  shown  how  he  can  readily  make  apparatus  to 
illustrate  them. 

^j  In  order  to  secure  the  fullest  educational  value  astronomy 
is  regarded,  not  as  a  mere  sequence  of  isolated  and  imperfectly 
connected  facts,  but  as  an  inter -related  series  of  philosophic 
principles.  The  geometrical  concept  of  the  celestial  sphere  is 
strongly  emphasized;  also  its  relation  to  astronomical  instru- 
ments. But  even  more  important  than  geometry  is  the  philo- 
sophical correlation  of  geometric  systems.  Ocean  voyages 
being  no  longer  uncommon,  the  author  has  given  rudimental 
principles  of  navigation  in  which  astronomy  is  concerned. 
^j  The  treatment  of  the  planets  is  not  sub-divided  according 
to  the  planets  themselves,  as  is  usual,  but  according  to  special 
elements  and  features.  The  law  of  universal  gravitation  is 
unusually  full,  clear,  and  illuminating.  The  marvelous  dis- 
coveries in  recent  years  and  the  advance  in  methods  of  teach-, 
ing  are  properly  recognized,  while  such  interesting  subjects 
as  the  astronomy  of  navigation,  the  observatory  and  its 
instruments,  and  the  stars  and  the  cosmogony  receive  particu- 
lar attention. 

^|  The  illustrations  demand  special  mention;  many  of  them 
are  so  ingeniously  devised  that  they  explain  at  a  glance  what 
many  pages  of  description  could  not  make  clear. 

AMERICAN     BOOK    COMPANY 

(181) 


ELEMENTS    OF   GEOLOGY 

By  ELIOT  BLACKWELDER,  Associate  Professor  of 
Geology,  University  of  Wisconsin,  and  HARLAN  H. 
BARROWS,  Associate  Professor  of  General  Geology 
and  Geography,  University  of  Chicago. 

$  I-  4° 


AN  introductory  course  in  geology,  complete  enough  for 
college  classes,  yet  simple  enough  for  high  school  pu- 
pils.     The  text  is  explanatory,    seldom   merely  des- 
criptive, and  the  student  gains  a  knowledge  not  only  of  the 
salient  facts  in  the  history  of  the  earth,  but  also  of  the  methods 
by  which  those  facts  have  been  determined.      The  style  is 
simple  and  direct.     Few  technical  terms  are  used.     The  book 
is  exceedingly  teachable. 

^|  The  volume  is  divided  into  two  parts,  physical  geology 
and  historical  geology.  It  differs  more  or  less  from  its  prede- 
cessors in  the  emphasis  on  different  topics  and  in  the  arrange- 
ment of  its  material.  Factors  of  minor  importance  in  the  de- 
velopment of  the  earth,  such  as  earthquakes,  volcanoes,  and 
geysers,  are  treated  much  more  briefly  than  is  customary. 
This  has  given  space  for  the  extended  discussion  of  matters 
of  greater  significance.  For  the  first  time  an  adequate  discus- 
sion of  the  leading  modern  conceptions  concerning  the  origin 
and  early  development  of  the  earth  is  presented  in  an  ele- 
mentary textbook. 

^[  The  illustrations  and  maps,  which  are  unusually  numerous, 
really  illustrate  the  text  and  are  referred  to  definitely  in  the 
discussion.  They  are  admirably  adapted  to  serve  as  the  basis 
for  classroom  discussion  and  quizzes,  and  as  such  constitute  one 
of  the  most  important  features  of  the  book.  The  questions  at 
the  end  of  the  chapters  are  distinctive  in  that  the  answers  are 
in  general  not  to  be  found  in  the  text.  They  may,  how- 
ever, be  reasoned  out  by  the  student,  provided  he  has  read 
the  text  with  understanding. 


AMERICAN     BOOK     COMPANY 


OUTLINES    OF    BOTANY 

$1.00 

By    ROBERT    GREENLEAF    LEAVITT,  A.M.,    of 

the  Ames  Botanical  Laboratory.     Prepared  at  the  request 
of  the  Botanical  Department  of  Harvard  University 


Edition  with  Gray's  Field,  Forest,  and  Garden  Flora $1.80 

Edition  with  Gray's  Manual  of  Botany 2.25 


THIS  book  covers  the  college  entrance  requirements  in 
botany,  providing  a  course  in  which  a  careful  selection 
and  a  judicious  arrangement  of  matter  is  combined  with 
great  simplicity  and  definiteness  in  presentation. 
^j  The  course  offers  a  series  of  laboratory  exercises  in  the 
morphology  and  physiology  of  phanerogams ;  directions  for  a 
practical  study  of  typical  cryptogams,  representing  the  chief 
groups  from  the  lowest  to  the  highest  ;  and  a  substantial 
body  of  information  regarding  the  forms,  activities,  and  re- 
lationships of  plants  and  supplementing  the  laboratory  studies. 
^J  The  work  begins  with  the  study  of  phanerogams,  taking 
up  in  the  order  the  seed,  bud,  root,  stem,  leaf,  flower,  and 
fruit,  and  closing  with  a  brief  but  sufficient  treatment  of 
cryptogams.  Each  of  the  main  topics  is  introduced  by  a 
chapter  of  laboratory  work,  followed  by  a  descriptive  chapter. 
Morphology  is  treated  from  the  standpoint  of  physiology  and 
ecology.  A  chapter  on  minute  structure  includes  a  discussion 
of  the  cell,  while  another  chapter  recapitulates  and  simplifies 
the  physiological  points  previously  brought  out. 
^[  The  limitations  of  the  pupil,  and  the  restrictions  of  high 
school  laboratories,  have  been  kept  constantly  in  mind.  The 
treatment  is  elementary,  yet  accurate  ;  and  the  indicated 
laboratory  work  is  simple,  but  so  designed  as  to  bring  out 
fundamental  and  typical  truths.  The  hand  lens  is  assumed 
to  be  the  chief  working  instrument,  yet  provision  is  made  for 
the  use  of  the  compound  microscope  where  it  is  available. 


AMERICAN    BOOK     COMPANY 

(174) 


DESCRIPTIVE 
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WE  issue  a  Catalogue  of  High  School  and  College  Text- 
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^|  For  the  convenience  of  teachers  this  Catalogue  is  also 
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